This has so many red flags.  Do not allow this woman to make demands. And watch very closely how your BF responds. Is he parenting?  Is he putting BM in her place?  Does he have your back?

You are right. You do not have to meet bm. 

Also, if you have been lurking for some time, I hoped you have picked up that a lot of bm's poison relationships with skids. Go on and expect that to happen.

So, long distance and you both have kids...who is going to move? If it is you, please make sure you know everything you need to before uprooting yourself and your children. Bait and switch happens often. 

This is up to BF to handle , you made your position clear to him and he needs to make it clear to BM that she isn't the boss of him anymore. Unless she wants to hand over to him the right to inspect all men she dates, she gets no say in who he dates and if she meets them. They are divorced. Not him and the kids.  

She's going to play her mind games. There nothing that will stop her. I'm sure I am safe in saying that there are many of us who, if we could turn back time, would never hand over our power to a carzy BM. The years of stress and hell we could have avoided.  I wouldn't meet her until after a wedding. She is turning this into a pissing match over who controls your man.  Why can't he say to her I don't want her to meet you BM?  Why is he so tempted to  drop the walls that he knows should stay in place to protect your relationship?  
She hurt your kids so that means YOU get to decide. The best foot to start out on is one of owning your power.  She wants to meet your first so she can figure out how to bad mouth you to the skids.  The skids can fill her in. Not the other way around.  

Do not allow his X any place in your relationship. She gets to make no demands. If she does, just laugh in her face and get on with the relationship with zero consideration of her at all. She does not get to demand to vet her X's new partner.  If she wants to, she can do a background check on you but does not get to demand to meet you.

Tolerate no crap from her and make sure your SO tolerates no crap from her either.

I would not agree to be vetted by BM.  If she is a person without integrity, as so many of them are, she will use the opportunity to pick holes in your character and behaviour, no matter if you behave like Mother Teresa.  The NPD BM in my life, started casting aspersions on me before she had ever clapped eyes on me, she told her daughters (then aged 5, 7) that I was a prostitute and had many men, not just their father!  I have been face to face with her only about 3 times in 18 yrs.  She has never had my phone number and I had caller display on our landline so if she ever called on that I would not answer. 

My advice is start as you mean to go on and draw very firm boundaries around any BM activity.  When we all start out, we want it to be nice and civilised with BMs - but this rarely happens in the cases of SMs who find their way to StepTalk.  Most of us are subjected to a high degree of PAS, and are subject to the often paranoid projections of high conflict BMs. 

The best foot you can start off on is for her to know that she has no control over you, your life or your choices. None. Zero.

Doesn't matter if she's met all her BFs exs and their new partners and parents and kids. Her life is not yours, yours is not hers. Do not allow her to ever think that she has any control over you.

Early on our relationship BM would call DH and scream at him for money, or tell him what an ass he was, or how she hated him, or whatever was bothering her in that moment. I took his phone and hung up. She called back, I hung up. He was terrified! He said that I'd just made it worse, that I didn't know how she was.

I told him that she had no power over me and that right now we, he and I were together and I wasn't willing to share him with her. If there was a real emergency, she'd find a way to get him, through his parents or have the police or hospital call. If he wanted to listen to her yell at him, he could take me home and call her back. But don't ever call me again.

It worked. She stopped calling unless it was something worth talking about and she even stopped yelling.

Do not do this. It's giving in to demands that BM is not entitled to make. It's best if you just meet her at a drop off or pick off, or just randomly.  I barely spoke to BM in all the years that SS was visiting, usually just "hello".  Whether or not your BF met her BF is of no consequence, that was her choice, and not required.

As for the mind games, yes, she's going to play them, and play them hard, for the entirety of your relationship - about both you and your BF.  Best to get used to that. With some kids, it really works well and they end up hating their stepmother, their father, or both.  Be prepared for that.

BM here never targeted me, but she did a fantastic job turning my SS against his father.

BM is demanding to meet me

BM is not the boss of you. If you don't want to meet her, don't.

Most likely, what she wants to do is size you up and get a feel for just how much she can push you around and if you will back down or stand up to her. Do yourself a favor, stand up to her right now, from the get go, and don't let her make demands of you or tell you what to do.

What a lot of these BMs don't like, is the unknown. Is the new GF a pushover? Can I intimidate her? Or is she a badass, who will not put up with my crap? Don't put up with her crap.

Now, BM over here has an MO of befriend, get someone's defenses down, then attack. I shut that shit down, immediately, letting her know that her little act wouldn't work on me.

In 24 years, I have seen her twice and talked to her 2 or 3 times (benign conversations). Haven't seen or talked to her once in the last 10 years, since my SD is now 29. She gave my DH hell, which affected me, but she didn't mess with me, personally.

This really is one of those, "start as you mean to go on" situations.

BMs like this will always use their kids, say things, and manipulate the situation, no matter what you do or don't do, so don't feel that you have to do something to keep BM from being high conflict or negatively influencing the kids. If she is that kind of person, she's going to do those things, anyway. It is not your job to keep her behavior in line, to make sure that she acts with integrity. She either has it or she doesn't.

This one is sticky. If your SO has already met BM BF, then it makes it look like you are the one with the problem meeting her. Here are some different scenarios. 

1. If you don't feel like meeting her yet, or not at all, just don't. You don't have to. Just know she will spin this to the kids. "She doesn't like me. She doesn't want to meet me, etc" 

2. Agree to "introduce yourself in person" and keep it at a neutral place with your SO. Short and sweet. Problem with this is you're opening a can of worms to anytime she wants to "meet or talk." If anything else comes up down the road, your SO can explain to her how y'all have met, but there is zero reason for y'all to communicate on a regular basis (just like with your SO and the BF I assume). The bio parents can handle talking about the kids. 

Personally, my SD BM never once offered to meet. I actually offered to meet her first, but she VERY defensively declined and told me to "never talk to her again." Here we are 5 years later (married 2 of those years) and I made sure she kept her promise... even though there has been countless times she has told DH she needs to "settle things with me"... Too bad. I think it drives BM even more crazy that she can't get a reaction of any sort out of me. 

There is no judge or court order on this planet that will make it a requirement bio mum gets to screen and interview girlfriends

i actually came to steptalk because of sd who was 22 demanding as per bio mum that i must be present at their first meet after she kidnapped the girls 5 plus years prior... 

i had 2 kids aged 2.5 and 1 at that point and being made to pack nappy bags, essentials and spend 3 plus hours driving for 3 selfish effwit stepkids didn’t sit well with me when these meets of so called quality family time were nothing more than sd rants on bio mum and stepdad reporting on daily life like we give a shit about them. 

Lucky for the many stepparents here who told me to end this shit with my husband. I told him i do not get ordered by a 13 & 22 yr old sd. Heck they think they can order me around regarding how i parent my kids.

those skids will see bio mum ordering you around and see it normal to order you around. You are the adult here, metaphorically speaking, keep your balls high until and not down where bio mum wants them so she can control you...

in my case bio mum tried to push things but me disengaging means she controls nothing that goes on in my household. Hubby has a firm rule he can have skid meets away subject to it not affecting our quality family time. Since skids treat him and us as strangers, not as a united family even with their dad, they are at the bottom of pecking order when our kids actively interact with hubby and love him unconditionally 

plus there are too many times where they cancelled last minute. If we have plans, they do not get changed for skids who are sd24.5, ss22 and sd14.5

When I started dating DH he had lied to BM about being in a realtaionship with me so when she found out she acted like she had all of these rights to know his personal business. I had met his son before I met BM and she was furious demanded to meet me immediately When i did meet her and saw what a complete train wreck she was I said you have to be kidding me. She wanted to be friends and I squashed that right away, then she thought i was a babysitter...nope. she actually would call and cry to me about how I supposedly broke them up and how i was ruining their "family". Yeah ok NUTJOB

We have been together for 5 years and this women is still a complete nightmare. DH still acts sometimes like she has him by the gonads becasue if she doesn't get her way with extra support she starts that you won't see your son BS. He has recently decided to file for primary custody becasue she is supposedly using drugs. I'm honestly hoping that he looses becasue I don't want to raise his hyper 10 year old that can't do any wrong in daddys eyes becasue he feels like he has to compensate for not being there 24/7.