We did a day trip to Glastonbury and Wells from Bath in October 2017. It is a nice day trip. On the way back, you can choose to ride through a scenic area called Cheddar Gorge.
The Cathedral at Wells is small but impressive and the small town is neat to visit.
Glastonbury is interesting, but it didn't WOW us.
After our stay at Bath and day trip as described, we drove to South Wales and Cardiff, stopping at Tintern Abbey and a couple of castles on our way to Cardiff. There are many, many interesting castles in Wales.
I think a day trip from Bath to Cardiff would be a bit much, since you wouldn't have a lot of time to see Cardiff Castle and the Museum of Welsh History, or Caerphilly Castle, a short train ride north of Cardiff.
Also, we visited Tenby for a couple of nights, before proceeding on to visit Penbroke Castle, where Henry VII was held before he escaped with the help of his uncle, Jasper Tudor. Tenby has an interesting history regarding Jasper Tudor, escaping in a tunnel to the port. Also, St. David's at the SW tip of Wales is worth a visit.
We spent five nights in South Wales and loved it.