Is she spayed? If she isn’t, I’d suspect something is wrong with her reproductive organs, for example pyometra (uterus full of pus). Drinking constantly is an observandum and often a sign of an infection somewhere in the body.

You could also check her scent glands as they might need to get cleaned.

Here’s a nice video on how to clean a rabbit’s scent glands, in case you haven’t had that experience before in your life:

how to clean scent glands

I’m glad she isn’t really constantly drinking! It’s a warning sign that can mean many things, that’s why I reacted. 

Can you tell what part of her the smell comes from? If it seems to come from the fur on her backside, it could be sth that will wash off. Some things can be combed off if you rub corn starch into the fur first, then comb.

You can bathe a rabbit if you absolutely have to, but it needs to be done very gently. I’d run up about two inches of lukewarm water in a plastic wash basin or something like that, then gently place the bun in the water hind feet first, then let the rest of the body follow. Gently pour water from your hands on the bunny’s back, avoid head and ears. Use a very tiny amount of organic shampoo or soap. Rinse again by pouring clean lukewarm water from a jug or a mug.
Afterwards the bun needs to be dried, first with a terrycloth (or even better, a microfiber) towel, finish if needed with a blow dryer on a low setting. If the weather is warm you might not have to use a blow dryer, although many buns seem to like it. All this obviously requires patience and calm movements and preferably an extra human for assistance. If the bun panicks, obviously stop.

If neither of your rabbits are spayed, it’s very doubtful that you will be able to bond them, and you will be risking injuries if you do put them together. Since Petunia is 7 years old, you, nor the vet probably would not want to spay her. Nella is past the usual age that most rabbits get spayed, but she would probably still do fine. But having just one rabbit spayed or neutered won’t work for bonding. Both need to be spayed or neutered.

If you do have to resort to a bath for Nella, two bar soaps that are very mild are Kirk’s Castille (unscented) and Clearly Natural (unscented).  You could cut off a small piece of the bar of soap to use.