I love Bath! I'm one who will spend several nights there and never get everything marked of my list.
The Jane Austen Centre is a waste of money in my opinion. She did not live in that house, they have none of her original items (lots of photocopies you could print off the internet if you want, lol) and it's way overpriced. Many enjoy their tea room for which you do not have to pay an entry fee. I'm not an afternoon tea person so I've never done it myself. I did do an excellent walking tour sponsored by the Centre a few years ago during the Jane Austen Festival (September) and if they happen to be offering that, I'd do it.
I love the museum at #1 Royal Crescent. It's a restored Georgian town home. The docents in the rooms are full of information and readily answer questions.
There is a very neat garden in Bath called Prior Park. It has one of the only surviving examples of a Palladian Bridge feature. It is quite a walk uphill from the Bath Centre to get to the entrance gate, then the park is essentially downhill. May would be a wonderful time to visit as I'm sure the flowers would be beautiful. I stopped at the Tourist Information office and got walking directions to the park but in retrospect it's pretty easy if you have a Bath map. There is also a bus route that goes by but I didn't mind the walk.
https://www.nationaltrust.org.uk/prior-park-landscape-garden
I also concur with the advice for using Mad Max for tours. I've done 2 with them (Stonehenge/Avebury/Lacock/Castle Combe and a day in the Cotswolds) and they were excellent. The driver guides have been excellent and they use the small 15-20 passenger vans. The competing Lion Tours I've heard good things about as well. In fact I understand that the founder of Lion is the ex-husb of Maddie from Mad Max. I would take either depending on who offered what on which day, lol.
There are also the Botanical Gardens at Royal Victoria Park in Bath. This has been on my list for several visits and I've always run out of time.
https://visitbath.co.uk/listings/single/the-botanical-gardens/
The Holburne Museum has some excellent exhibitions so check to see if they are showing anything that is of interest to you. I saw a Canaletto exhibition there several years ago and it was amazing.
You might consider a day trip to Salisbury which is another of my favorite cities. The cathedral is magnificent and the Close around the cathedral is unusual. There is a very nice museum there but it has a lot of Stonehenge stuff which might not be your cup of tea. They also have good exhibitions - saw a Constable in Salisbury one there a few years ago with was fabulous.
I've stayed at Kennard House B&B (new owners since I stayed), Henrietta House (right across the street), Brooks Guest House (on an RS tour) and the Francis Hotel on Queen Square. The only one I'd not return to was the Francis and although the room was very nice it was just a way bigger hotel than I really enjoy.
For the birder - walk along the path on the east side of the River Avon. Get on at Parade street and walk south. You'll see a large church across the river and there are generally Peregrines who nest here. I was there in May in 2018 and some of the local birders had a spotting scope set up at the point I think I have marked on this googlemap link. It was terrific fun talking to them!
https://goo.gl/maps/cDCQjYQ2UDiUcAct7
https://hawkandowltrust.org/index.php/conservation/projects/urban-peregrine-project
https://www.stjohnsrcbath.org.uk/index.php/falcons/falcon-webcam
BTW, be on the lookout for falconers with Harris Hawks in areas where they are trying to control the pigeon population. My brother and I were startled in Canterbury Cathedral cloisters when a Harris Hawk flew by and perched near us just outside as well as at Kings Cross Station. Very cool!
You are in my favorite area! Have a terrific time!
