I don't mind getting changed but I won't intentionally have a shower or bath in front of an animal, if they wander in during bath time that's fine (I lock the door (they're smart enough to open the door if it's not locked) when it's a shower; mostly due to a shower actually being my more relaxing time and it's thought time). Apart from that, I'm fine with it. Animals are generally quite smart but they don't feel any shame over you seeing them naked or them seeing you naked; so why should you?
I feel less bashful/modest around animals than I do humans, animals don't judge you. To them, you're you; no matter what you look like or whether you're naked or clothed.
Also, do it. The sooner the better, you'll feel better for it and even if she says no; you've moved on. Also the Gym is a horrible and intimidating place until you've been once or twice*. Then it's actually kinda nice, you get relax time; the pain actually feels kinda good since you know you're working off calories and there is generally a positive attitude. Probably a good idea to get a personal trainer to give you a look around and tell you what to start off with and follow that. Just to be clear, I'm not suggesting signing up permanently for a personal trainer but one quick session should be sufficient. [My Gym does $30 per session and it's genuinely helpful.]
*The sooner the better applies even more so here, in a few months you could've dropped a coupla pounds (or gained some muscle). Procrastinate and you'll kick yourself for the wasted time.