This is short notice as only just seen your post but you are not leaving any time for any delays in transport time from either your home, train, taxi/bus up to the Uni. Traffic in Bath can be horrendous during peak times and the trip up to the Uni can take anything from 10 mins to 25 on really busy days.
Options: call the number given on your interview letter and ask if there is any option for a later appointment.
If not I suggest option 2 which is to see if you can stay in Uni accommodation overnight (seem to recall cost is £60) and go down the day before.