Definitely do stay another couple of nights in Bath. There is so much to do, IMO!! I stayed 3 nights previously and this trip I am staying 5 nights, altho 3 of those nights are on the Best of England tour, so one full day is in Wells and Glastonbury. If you decide you want a day trip from Bath take a look at Mad Max tours from Bath. I think South of England includes Salisbury and Stonehenge, but they also run some tours to the Cotswolds if that is of interest to you. Otherwise to me there is enough for 2 full days in Bath. Do take a look at the Bath Abbey website to see if there is some kind of organ concert going on when you are there. When I am there in a couple of weeks it is the Jane Austen Festival which has some special presentations and JA focused walks. Not to everyone's taste, but it suits me!
Lodging-wise, in 2013 I stayed at the Kennard in Bath but they have changed ownership. It still looks like they are getting excellent ratings on Trip Advisor. When I stayed there the breakfast room was so beautifully decorated as a garden room I wanted to take it home! It was not inexpensive though. Also know that in Bath the prices go up significantly on Friday and Saturday and the accommodations often have a 2-night minimum for those nights.
On the RS tour in a few weeks we stay at the Brooks Guesthouse and I will stay there a couple of nights before so I don't have to move around. So far they have been very responsive. When I initially made my reservation there was a single room for one of my nights and only a double room for the other night. I went ahead and booked that way, then had an email exchange with them regarding being wait-listed for a single. Imagine my surprise when they actually did email in June to tell me a they had a single cancellation so they will put me in the same room as on the RS tour for all of my nights. Excellent news as I plan to do some major sink wash during that time, lol!!
Last time I walked by 3 Abbey Green which is in a great location and looks terrific from the outside. No opinion of inside, though.