I don't have much advice, other than to note that menstrual hang-ups seem really common with CODs.

My SD used to use toilet paper, rather than ask for pads (although I made sure she know where pads were kept.) But at least it all got cleaned up. 

Does she know you find them? Does her dad and BM know she started? Does she use any products you have bought her?

Time to have a frank discussion with her. Nothing to be embarrassed by, but the hiding has to s stop. Tell her that if she continues to do it, you'll have to talk to her parents about it WITH her. Not out of shame, but because it's not sanitary to have dirty underwear laying out. Find out what's causing this with her and address it from there.

Picardy must be right about the problems with CODs.  My SD was late to begin her periods,  her girlfriends had already started.  We bought supplies, had discussions, talked about the disposal method.  She finally got her period, so happy.  A few days later, we started seeing sewerage water coming up in the basement, eeewww.  DH called the plumber who reamed out a bunch of used sanitary pads.  I was tearing my hair out because of the exasperation and expense but Disney Dad thought it was just a little excusable error.

A month passed and next time, she didn't flush them, just kind of left them draped around in the bathroom. Double eeewww!  But Disney Dad explained, "She's just proud she started".

How old is the SD? It could be shes not sure how to use the items, so instead just figures the underwear will do what they need to. If she's uncomfortable wearing a pad...and who isn't...they have underwear that has a pad built into it. I bought these for BD because she had leaked a few time and it embarrassed her. I think they are called thinx and they have them for tweens.

My SD started hers pretty early- 10. She left dirty pads in her room as well as underwear. I just waited until she was alone and was blunt, I told her she needs to make sure they are going in the waste bin (pads) because it's disgusting and making sure her dirty underwear get put in the dirty clothes. She said "ok I'm sorry" and it never happened again. I tried not to make a big deal out of it but being honest as well. If she is super young I don't think that cleanliness part comes easy lol. 

I'd use the "in this house" line to start the discussion. I mean really, she will need to know what to do when living as an adult, sharing space with others. If no one else will tell her than go ahead and set the standards in your home.    Go ahead and buy her a body book and leave it in her pillow so she has a reference.  If you set her clear on what she needs to do at your house and she still chooses to not listen, bag her stuff up and send back to BM with SD and let her mother deal with her laundry.   

You have to be direct and tell her exactly what she needs to do and what is expected of her. Maybe do it in the car rather than face to face. 

She obviously has some questions but isn't asking them so just prepare a little lecture about PMS symptoms, how to use and dispose of pads, talk about tampons, cups and thinx as options but she needs to ask you or her parents for them, and laundry tips for blood stains (oxyclean!). Just be matter of fact about it.  

If you don't want to do that I'm sure you can find a youtube video about it. 

Kids don't come preprogrammed, you have to teach them. CODs have so many issues in part because both parents assume the other will take care of things and then neither do.

I was very direct with OSD who was not exacty the cleanest, neatest teen (understatement).

I was very clear that NO flushing of products was to be tolerated (we have a septic system) and what would happen if she did and things backed up. I also had a separate conversation with DH about it telling him exactly what he'd be responsible for if she flushed things anyway and we had a septic issue.  Unfortunately we DID have a septic issue, OSD was grilled by DH, and it turned out to be a broken pipe - DH apologised, OSD said "told you so!" and we moved on (OSD was very sneaky about hygiene and cleaning so we didn't really believe her until it was proven).

I was also clear that there was an appropriate disposal method for products in this house and she was to follow them. I also told DH this. If she neglected it, I'd find out and HE'D have to deal with it. This only happened once when she left a dirty pad in her room (for the 2nd time I think). DH had to deal with it.

It resolved after that.  However, when she left the house we found horrible filthy underwear in her laundry (one random pile one in her laundry basket) that she had worn many times it looked like and never washed (she didn't do laundry). DH had to throw those out. I also found that she would unwrap items she took from the cupboard and throw the wrapping INTO the cupboard instead of the trash. There was a huge pile of wrappings burying the products.  WTF?

YSD14.5 still has not had hers, she knows where the products are and to let me know when she gets it so I can make sure she has what she needs here. There's no running out of stuff in our house, no need for it. She's clean and neat so I think she'll be fine.

Underwear but we wash it. 
leaving it to ferment and the stench is just inexcusable... dumping pads and not putting it in the bin is nasty.

i have always had heavy flows and 1st 2 days of my period are the heaviest and i tend to have leakages sometimes but i use tampons to control the flow.

any bloody underwear are washed right away...

i just can't ever imagine my hubby excusing crap like this and sayin "oh she just proud!!" Because if i displayed bloody pads out in the open he'd be turned off sex immediately 

We've been dealing with this exact same problem. I just started throwing them out after the first and second conversation. They both ran out of underwear so they were responsible for buying them. No major issues since.