Sunday January 5th - Arriving in the morning via train. Maybe just hang around Bath, go to the "Baths" maybe take train to Salisbury to see the Cathedral?
This is too much for one day, in my opinion.
You would be better off doing your time in Bath, then taking the train (short ride) to Salisbury to stay for two or three nights.
Stonehenge (which you mention wanting to see on Jan. 6) is right outside Salisbury. You take the Stonehenge bus out from the train station or the center of town (near the Visitors Center) to visit Stonehenge while staying in Salisbury. The same bus brings you back to town after you get your fill at Stonehenge.
On the way back to town on this bus ride, the bus stops at Old Sarum. You may hop off to see this and hop back on the bus later if you wish.
You will want to see Salisbury Cathedral. (As mentioned just above, by BillS719) It's a magnificent piece of architecture. Salisbury is a fabulous medieval small town; worth walking around to pick out the old buildings. This you won't get in Bath; its buildings are mainly Georgian.
For some reason I am stuck on going to Cotswolds....We could also potentially do Cotswold from Oxford.
YES to going to the Cotswolds from Oxford. It's easy. From Oxford, you take the train a short distance to Moreton-in-Marsh, a lovely Cotswolds town. Catch the Go Cotswolds tour from Moreton. You will get a good taste/sampler of the Cotswolds in this day tour.
https://www.gocotswolds.co.uk/product/cotswolds-in-a-day/
I wouldn't try to do everything from Bath. However, a trip to Glastonbury and Wells from Bath IS a good way to do that. There are coaches (buses) that leave from Bath and go to these places. However, we will have to wait until one of our experts (isn31c, Stuart) chimes in here, as he is the one in the know about coach or bus schedules.
I would enjoy Bath fully while you are there, then move on to Salisbury for 2 to 3 nights, then move on to Oxford for 3 or 4 nights. I have not looked at any of your other threads/postings, so I don't know what your full schedule is.
If you wanted to add more of the Cotswolds, I would consider hopping off the Go Cotswolds tour at the very end and staying a night or two in Bourton-on-the-Water, a beautiful village where pretty Cotswold stone bridges cross the crystal waters of the River Windrush.
If you're wanting to add more in the northern Cotswolds, you might consider a night or two in Stratford-Upon-Avon and also in Warwick, with its mighty Warwick Castle.