We will be visiting in London in mid-August and were thinking of spending a few days during the week in Bath.

What can we expect in terms of crowds?

What would you expect in the US at a tourist attraction ???????
I guess you have your answer

We were there last August and found that Bath was quite crowded during the day but much less so in the evening. We really enjoyed taking an evening tour of the Roman Baths as they were beautifully lit and not at all crowded at that time. I recommend the free walking tours the city offers during the day and the evening Bizarre Bath walk (not free but hilarious.) Have a great time!

The only place the crowds will be bad is in the confines of the Roman Baths/Pump Room. But since you are staying overnight you can avoid that by either going right at opening time before the day trippers/coach tours arrive, or in the evening after they've left again.

Sure there will be crowds out and about - but the town absorbs them pretty well.

Bath isn't primarily a tourist attraction: it's the economic centre of a reasonably affluent miniregion - with a few things interesting to tourists on the side.

This means that, in most of the town, crowds form and disperse - and traffic gets congested - as you'd expect in any other medium size European town: most crowded round the main shops during lunchtime and weekends, traffic most congested during commuter periods. And the whole thing, net, at a slightly lower level during August since lots of people are away.

Bath absorbs pedestrians reasonably well as janisj says: it doesn't absorb cars ever really, except late at night, though traffic's less of a problem in August.