Hi
Bath has 3 Park and Rides. They are at Lansdown (N), Newbridge (W) and Combe Down (S) of the City. The details are here: bathnes.gov.uk/transportandstreets/Parking/p…
The big chains aside, most city centre B&B's ought to be able to offer you a visitors parking permit (circa £2/day, but others will clarify) so you can drive about in a local residents parking zone to find a parking space (I know this is more tricky in some zones, so I flag it).
If you are planning things last minute, don't rule out Lastminute/laterooms/wotif.
Otherwise I would first go to the accommodation bookings on www.visitbath.co.uk and Holiday Inn Express and Travelodge.
A lot cheaper (and on a regular bus route) would be the YHA (with kitchens and family rooms).