I live in Bath too and I love living here. I don't think it's anything to do with it's "whiteness". I love it because:
The city centre is beautiful.
There are great shops.
Lots of history. (I love history)
Great food.
Lots of lovely places within easy reach.
Beautiful countryside.
Lots of art galleries. (love art too)
It's also ridiculously busy at weekends, in the summer and at Christmas and the local government hate car drivers with a passion, so there are downsides.
We walked around the local cemetery recently and there were a huge number of graves with non English surnames, which seems to suggest that other cultures having been making their home in Bath for a long time.
We've moved around a lot and even lived in a small town that was a lot more "white" than Bath is, but I'm happiest here than I've ever been.
Having said that I could very happily live in Bristol too, which is much more multi cultural. We know it well because our daughter lives there and I love it's buzz, but the traffic is worse than Bath and I just couldn't take it.
I have to say that your inverse snobbery is showing username and you sound a bit ridiculous.
My roots are firmly working class, but I'm not going to apologise for being a middle aged, middle class (sort of), art loving history buff who happens to find Bath lovely and not at all weird.