No, don't try and bribe them, it won't work and you will be out of pocket.  My advice to you and to any new step mother would be, have a come to Jesus with their Dad and tell him that he MUST have your back with regard to the step kids behaving respectfully to you in your home, this is a deal breaker.  They don't have to like you and probably never will.  I had the same problem, (although DH and I didn't meet until well after he'd left NPD BM) their bio mother badmouthed me to her kids before she'd ever clapped eyes on me.  Fifteen years have passed and I still don't have a relationship with them, because of that.  

Step parenting is hard as hell, and if your partner doesn't support you, it is going to be a darn sight harder. 

DH and I were not intimate before he and BM were divorced. They had been separated for 5 years when I met him...but kept trying to go to counseling and work it out. We were merely colleagues and partners on a work project. I met him 5 years before we got married and 4 years before we started dating, and he and BM were long over before we started dating. 

She STILL took it upon herself to tell her kids (at ages 10, 12, and 14) that DH had been unfaithful to her and that's why they couldn't work it out. This fact just came out this past January when I took YSD to a concert...she was asking me if it was true and told me that, even if it was, she felt angry at her mom because she "didn't think she needed to hear that about her dad at 10." 

Say all this to say...I was mostly just myself with the skids, and I think it turned out OK. Of course, it helps that I didn't KNOW BM had been bad-mouthing DH (and me, I guess) behind my back. Often, when the BM bad-mouths you and the dad, the kids reject you and their dad...but, sometimes, they don't and it backfires on the mom. No telling what will happen in your case...but the worst thing you can do is over-compensate out of guilt.

I would just be kind to them.  How old are they?  If you're buying yourself a treat, you might want to ask if they want one too, but I wouldn't go out of my way to "bribe" them.  That rarely works, and it looks like you're trying too hard.  

NOPE no gifts just yet. Just be pleasent and step back a little. In other words dont try too hard.

During this introduction time you will learn very quicky if boyfriend will stick UP for you or throw you under the bus. KEEP YOUR EYES OPEN wide. And do not justify any action that doesnt feel right.

"oh, the kids really didnt mean to call me a witch. OH boyfriend doesnt see the kids a lot so he over looks stuff'....."I KNOW I put my makeup back in my makeup bag...hmmmm, it's missing. MAYBE I threw it in the trash"

"ITS ok Brandon, you didnt mean to drop my Great Grandmothers bowl from 1890'" "OH its ok sally, you didnt mean to drop my phone in the sink filled with dishes". "OH it's ok Tristen, I am sure my cat will come back they usually do...YOU didnt mean to stand there with the door open......

stuff like that. Your boyfriend should address wrong behaviors right away and he should ALWAYS expect his kids to treat you with repect. Thank God my husband did. Their poor behavior continued but DH always stood up for me. Pathogenic Parenting to the max...

GOODLUCK

Most of us make the mistake of trying too hard. Don't go there. Definitely no gifts. No matter how your relationship started, the kids need to be as respectful to you as to any other adult. They may forever dislike you and blame you for the breakup of their parents' marriage, but you don't need to be best friends. It's way easier for them to blame you than their dad.

If all you ever get is politeness, that's good enough.

Listen, the (age appropriate) truth and being humble can get you pretty far with kids. 

But double up on that #humble part. If they hate you, that’s their right and you know why. Just try the best you can to be who you are and let them come to you when they’re ready. 

Take this from someone who still after 15 years has a hard time choking out a sentence to my father’s mistress. My father who I did not speak to for 10 years because of the toxic ivory surrounding him. If she owned her behavior, it would be water under the bridge. She HAS been humble, at times helpful from a distance and she leaves me alone while I figure out how I’m going to navigate this-and I am 100% cool with that. I am pleasant, polite and try to be my normal self around her but I have a VERY strong reservation in the pit of my stomach about her because she never really owned it. If she owned it and apologized, then I would feel a lot more at ease-but she doesn’t owe me that, nor do I NEED it to get on with my life. It would just help. 

Your job is to have a fun day at the zoo, enjoy SO and the kids company and look at the animals. Dad's job is to buy them sweets, lunch and zoo toys if he wants.  

Your SO's job is to make sure his children are respectful of his choice of partner regardless of how your relationship started. If he cannot make that clear to the children then the entire dynamic will suck for you.  Being the other woman has so much stigma attached and grandma and BM are making sure that you wear that scarlet letter prominitely.  Go in with eyes wide open. If SO is like most of the Disney dads discussed on this board he will literaly do anything to assauge his guilt w/his kids, even moreso since he was likely responsible for the breakdown of the marriage. Sadly men in this position have no problem throwing their women under the bus in order to preserve their relationship w/their children.  

You identify as "Just a girl" but in Step world you're going to be labeled as The Other Woman, Homewrecker, Gold digger, Sl*t, Hoor...and so on. Believe me, I'm not calling you any of these things. I've been called a few of these and I have NOTHING to do w/DH's divorce.  Women are always the villians in these stories and men the poor helpless victims led astray.  Brace yourself for a whole lot of ugliness if you choose to continue in this relationship.  

I was a wife who divorced my husband over a mistress and the hurt and betrayal was horrible.  BUT, I didn’t want my children to feel the hurt, be mad or be even know about the reasons,   Life moved on and he remarried and cheated on the beloved step mama with mistress who turned into wife 3.  My daughter made wife 3 life a living hell and I mean living hell.   It was so bad I did stop couple of things going on because her father would do absolutely nothing to stop her.

the one thing that will always stick in my mind is whe I was telling my daughter to stop it, now, your are hurting her feelings and causing more hurt.   She looked he square in the eye and said  “why?  That bitch didn’t care about my feelings or beloved stepmoms feelings or my little brothers  feelings when she was out with daddy.  Don’t ever tell me to care about that trashy bitchs feelings”. Needless to say, wife 3 didn’t last long and daddy always got a free pass.  She’s grown now and and turned out great, still gets sad over her daddy’s and beloved step mamas divorce.  She is still close to her and her little brother,   She will always love her.   We all did 

I would say that it is highly dependent on the age of his kids.  If they are very  young.... you have a shot at a decent outcome.  The odds of a decent outcome are inversely related to their current ages (age during the affair stage of the relationship with their father).

From your OP it seems that they are quite young.  In that case a small gift may be appropriate.  If  they are much older than ~8... don't bother. It will  only set  you up to have it thrown back in your face (probably only figuratively) and for a ton of manipulation and drama later.

While I have long maintained that facts are neither good nor bad and merely facts... The adulterous nature of your relationship is one fact that will bite you and your SO in ass for the entire duration of your relationship as far as his kids and XW are concerned.  While there may be some mitigating details involved the odds of a good outcome with the kids and the X are decidedly slim.

I am fortunate that my own parents will celebrate their 56th anniversary next month and neither have (to my knowledge or the knowledge of the other) cheated... if one or the other of them had and moved on with their adulterous partner I would be their worst nightmare and I am 54  years old.  I suppose that may be a downside of raising children with morals, standards and character... particularly for a parent who has none.

Not that I am judgemental or any such thing. 

You don't say how old the kids are, but they might see right through the gifts and sweets. It will be like showing them you're desperate to be accepted and that will give them the upper hand and make it seem as if you have something to atone for. Trust me, skids are sharks when they smell blood! Try to normalize the relationship from the start with the expectation that they will be respectful without you buying them off.

Just be kind and step lightly.

But a little advice...I wouldn't make the first outing an all-day event. If they are old enough to be stressed about meeting you, especially knowing what they know. The tension will be high for all of you. Keep it short and sweet. If it's a long journey to the zoo and there's a bad vibe, you will have to endure that bad vibe the whole way home. This means there will be plenty of time for any of the skids to have a meltdown and you'll all have to get back in that car for the long, awkward drive home. I wouldn't plan anything longer than two hours total time together.

When my SD repeatedly had meltdowns that resulted in tantrums (and by the way, ha, ha, she was 20-plus years old!), our therapist suggested very short outings so there wasn't time for too much tension to build. Ten years later, I took it one step further and disengaged...but that's a tale for another day