Try keeping about an inch of water in the tub...this will keep her out of it.
Also...if the kitten was living in a shelter where she simply pottied through the bottom of the cage, she won't know what to do with a box. So you can have an empty litter box next to the tub, then each day add a little litter until there is a normal amount in the box.
Dodo is right about the introduction, so if they don't get along you may want to seperate them for a while and then re-introduce them properly. Also, if another box doesn't do the trick, you may want to try confinement to one room with a litter box at one end and her food on the other end. Cats don't like to do their business near their food so she should prefer the corner with the box.
When my cat had kittens recently, and the kittens started litter box training, the mommy stopped using it! I was horrified, she started using our bathroom sink instead.
All of the people here said they thought she probably didn't want to share. I went and bought an extra box, and confined her to a room with it for two days. She has been much better and the problem is solved. I think Donna is right when she says to get another box and see if that does it. It worked for me, and I really think cats dont like to share!!
My 5-month-old kitten pooped in the bath tub twice - once after I forced her to eat a medicine tablet. She expresses her dislike this way (or peeing around the house when she doesn't get enough attention, a real pest!). Now I close the bathroom door when I have to do something she doesn't like, and after that play with her a lot to distract her and make her forget.
I think jealousy plays a big part in your case, but first check that your cat is healthy. Sometimes when they are not well they eliminate out of their litterbox.