pls help check if I would have enough time for all these plans in Oxford

A few points:

Are you planning to pick up a hire car in Bath and then drive it to Oxford? If so, where will you park it? Many hotels in Oxford have little or no parking (city-centre parking is exorbitant and the one-way system is tortuous). You may need to allow extra time here.

I have not been into Christ Church since they started to charge a lot to enter on the back of the Harry Potter films. I suggest you look on Tripadvisor to see how long people typically spend there. Bodleain tours are well worth it and book the 90 min tour if you can, if it's not available then the 60 minute one.

Many of the things you want to see are close to each other (eg the Bodleain and covered market) and you can see quite a lot in a short time. You mentioned New College: it and many other colleges now charge for admission but not all do. See link below

https://www.ox.ac.uk/visitors/visiting-oxford/visiting-the-colleges

Unless you have a particular desire to see New College, I'd suggest visiting one of the colleges that is free or charges less. Wadham College - near the Bridge of Sighs - is free and looks like what many people expect an Oxford College to look like in that being only(!) 400 years old the buildings have not yet burnt or fallen down, which was the fate of many older buildings in Oxford.
In any case, do visit the Turf Tavern whose entry is down a narrow alley more or less under the Bridge of Sighs. It's supposed to be where Bill Clinton didn't inhale!

I love Oxford - have a great time.

To gain a bit more time you could go to Choral Evensong at Christ Church at 6.05pm daily. At least you will see the building, if not tour it.
Or achieve the same thing with morning prayer or Eucharist at 7.05 or 7.35am respectively.

On Day 2, check the time of the services at St Mary the Virgin - according to their website, they have a choral communion service at 10.30. This is unlikely to finish before 11.30 and it may be nearer 12 o'c;lock by the time the church is clear of worshippers and open for visitors. At 3.30pm, they have a choral evensong. Again the church will be closed to visitors just before rthe service. You won't be allowed to go into the church as a sightseer during a service.

The Bodleian Library tours (the 90 min ones that let you see inside the actual library) are only once a day on Wednesdays, Saturdays, and Sundays, and only in the morning. In that case you would have to go on your second day. You can find all the available times here: https://visit.bodleian.ox.ac.uk/tours/library-guided-tours

They go on sale one month before the tour date and sell out pretty much immediately so would recommend figuring out the day they go on sale for the date you want and logging on straight away. Good luck!

thank you everyone! I didn't consider the parking challenge in Oxford before reading the tip here! And I did email the library and they replied very promptly -- there will be only 14 tickets released each day 3 days a week and they implied it's not wise to build itinerary based on the assumption that it's easy to secure tour tickets successfully. I think it's a sensible point and would give up that assumption. With that, the revised itinerary becomes:

Day 1 (Fri). train to Chippenham, pickup car, drive through Cotswolds to Oxford -- find parking outside the city --- i.e. we will skip Bath this trip
Day 2 (Sat). full day in Oxford: Christ Church college tour, University and city tour, university church of St Mary the virgin Ashmolean museum of arts and archaeology, One other college (stretch and optional if running out of time)
Day 3 (Sun). drive from Oxford in the morning to Peak District-- either to stop on 1-2 villages along the way, or just allocate an extra afternoon to Peak District.

There are 3 or 4 “Park and Ride “ car parks on the outskirts of Oxford from where you can get a bus to the centre. Parking isn’t free, nor is the bus so you may want to see if your accommodation has any parking available and compare costs.

If you do drive in Oxford beware of 20mph speed limits and bus lanes.

Most convenient of the 5 Park & Ride sites for your itinerary is probably Pear Tree to the north of Oxford although Redbridge would also do.

Seacourt to the west of Oxford should be avoided at present as it doesn't have a bus service right into the centre because of a long term road closure.