Can Bath, Wells and Somerset all be visited in a weekend

Yes, it is of course possible.
I am slightly confused about your terminology. Somerset is a county, Bath and Wells are both towns in Somerset. Where else in Somerset apart from Bath and Wells anre you planning to visit?

Thank you for your reply. I apologize for the confusion. Would you kindly make a recommendation on where to stay in Bath and what other city/place you would visit on a 3 day weekend in Somerset county?

As well as Bath and Wells, I would visit Glastonbury. A somewaht unique small town, famous for the "Glastonbury Tor", a hill which was once an island in the middle of a swamp, with a tower on top. Famous for Arthurian legends, medieval pilgrimages and new age people

Try Brooks Guest House on Upper Bristol Rd in Bath. Not in the center of town, but close enough to be walkable to the main places you would want to visit there.

As for the original question: Glastonbury and Wells can each be seen in about half a day, and because they're so close together, they make a good pair to see on the same day. If you go to Glastonbury and Wells on Saturday, then that leaves whatever time you have on Friday and Sunday to see Bath. That's probably enough, if you leave Oxford on Friday morning and return on Sunday evening.

As for other places to see, Cheddar (home to the original Cheddar cheese, which in my family's opinion is very good) may be worth a quick stop. Check the hours of the cheese shops before you go, though - they might open later or close earlier than you would like.

The Mendip Hills have some great scenery and good hiking, if you like that kind of thing. Or you can drive through them, if you're not afraid of one-lane country roads.

Just southeast of Bath - about halfway between Bath and Salisbury - is the village of Edington. The church there is amazing (and it's close to a beautiful white chalk horse)

Keep in mind that a " weekend " or as used to be said " A Saturday to Monday " is not that much time , and you will have the logistics of drive time and finding a car park which are time consuming . Wells is relatively easy for parking and the cathedral is one of The UK's finest . Each time I visited , I spent the better part of the day there . Bath will require a full day , at the least . The Roman Baths take a fair amount of time , and the Parade Gardens and The Abbey are worth lingering . ( The Abbey's fan vaulted ceiling is second only to King's College Chapel in Cambridge ) . http://www.wellscathedral.org.uk/

We stayed at the Apple Tree in Bath last month. It was very close to downtown, well priced, clean & friendly. It proved to be an excellent base to explore Wells, Glastonbury, and Cheddar.