You can use the disposable diaper bags to put them in and then tie closed. If that doesn't work due to smell, then you can try putting the underwear into a ziplock bag and then into the disposable bag.
We also use the plastic grocery bags and tie them shut tightly, just like we do with the litter from the cat litter box. Then, straight to the outside garbage can they go.
I use a diaper genie. They are made for baby diapers but work fine for adult diapers. They aren't cheap....about $30 at Walmart...but I see them in thrift stores all the time for $10.
Oh...she seems to have trouble pushing them all the way down, but she puts them in there, and every time I go to the bathroom, I check and push it all the way down if necessary.