I agree with all the answers and I would like to add two other reasons:

I think Anne is always a little bit depressed or melancholic since what happened with Frederick. So she likes the calm, loneliness and fresh weather of the country where she is not reminded of everything she lost and/or could have had with Frederick. Bath is bright and lively, so everybody expects you to be happy and social. "Anne, though dreading the possible heats of September in all the white glare of Bath, and grieving to forego all the influence so sweet and so sad of the autumnal months in the country, did not think that, every thing considered, she wished to remain". Depressed people tend to prefer quiet and cool places rather that hot and crowed places.
Also Bath had two main purposes at that time: to show off and for young women to find an husband. Two things that Anne doesn't like as she is an honest and true person and is still in love with Frederick. She doesn't like fake relationships so Bath is not her place. NB: Sorry for my english!It's not my native language.