As far as I know there are only 2 places where you can bathe in the spa waters. One is the Thermae Bath Spa, a municipal owned complex, and the other is the spa at the Gainsborough hotel. The hotel used to be a hospital which used the waters for treatment.
Reviews of the Thermae spa are extremely mixed. Some people like it and others hate the experience, finding it too busy and lacking any kind of luxury feel. I’ve been a number of times and actually really enjoy it despite also agreeing with the criticisms! The rooftop pool gives fantastic views over Bath. I would definitely say to go midweek during the day.
I have also been to the Gainsborough spa. This is within a luxury hotel is a very different experience. It’s not massive but if you want to bathe it’s a good option and I really enjoyed my time there.