I wouldn't put a collar on your kitten. It is too dangerous especially since kittens get into things. If you take her outside, I would do it on a leash anyways so nothing happens to her. She is too little to be outside alone anyways. If you do decide to get one though, get a breakaway so if she gets caught on anything, she can break free. There have been cats that have hung themselves because their collars get caught on something when they jump.
As for the peeing in the bathtub. Could be a few things.
1) Try to keep her confined to a small room (the bathroom is a great place esp since thats where she is peeing) and put a litter box and her food and water and some toys for a couple days. This will retrain her.
2) If you have just her you should have 2 litterboxes. You don't need to buy fancy boxes from the pet stores either. They make disposable ones, or just take a few cardboard boxes and cut the sides low enough for her to get into.
If htere are more litterbox options she may pick her favorite.
3) you can mess around a bit with different litters and different boxes, she may dislike something about the ones you are buying. They also make Cat Attract litter.
4) Is she spayed? Female cats can spray at this age, she may be maturing and marking her area. If it is spray that she is doing into the bathtub, spay her immediately before she starts doing this all over your home. Vets can spay at 4 months and younger, so if your vet won't do it then look around for one that will. There are low cost clinics too.
5) LASTLY, she might have a Urinary Tract Infection. Is she not using the litterbox at all? Or just not peeing in it? She may want 2 boxes, one for pee and one for poo maybe. A UTI can ONLY be determined by the vet. But try some of the other things I mentioned first.
Good luck, ask if you have any more questions! Glad to help.
PS. At least she is going in the bathtub where you can wash it down the drain.