my daughter started freaking out in the bath tub a little earlier then yours, but her freak-outs were about her hair. she was perfectly fine until she was able to sit up...then she wouldn't cooperate when rinsing the hair, so she's tilt her head down (refusing to look up to not get anything in her face) and she would start to freak like i was trying to drown her when i would cover her eyes slightly and pour the water over her head. she's 2 and STILL does that, but now i just do it as quick as possible and sometimes it works, sometimes it doesn't.
another way for me to get her to allow me to wash/rinse her hair is to bring dolls in the tub and starting whatever i'm about to do on the dolls, then do it to her. and while i do her hair, i have her continue to do what i'm doing to hers, to the dolls hair. this way she's a little better, but it doesn't always work. as for taking a bath with her, you could put on your bathing suit and get in, then ask her to get in with you...maybe that will help. if not, you can always try the dolls. take her in dressed with dolls that can go in the water, run the bath and have her give them a bath, but tell her as she's bathing her dolls that she has to take a bath also, whether it's with, or after the dolls are done being bathed, either way she HAS to take a bath. this could work really well for you, but like my daughter, you have to understand it may not always work. be patient, and when it works, be greatful for those dolls :o)