Parking in Bath is limited and can be expensive. If you are planning to stay overnight, I recommend you book a hotel or b&b with off-road parking. This may mean you stay a 5 - 10 minute walk from the city centre, but it is well worth it.
If you are visiting for the day, try the park and ride scheme that the council operates. Driving around Bath looking for the few parking spaces there are takes a lot of time (the roads are a nightmare!) so this will save you a lot of stress in the long run.
If you can't avoid bringing your car, there is a reasonably sized car park near the Royal Crescent.
If you come by car to Bath the best thing to do is to use the Park n ride service which is signposted as you come into the city.Don't use the University one , unless it is a Saturday. The one we used is called Landsdown Road. YOu pay about 2.20 per person to ride the bus into Bath and the parking lot is free. The bus is comfortable and frequent and drops you right down town near all the major sites. Easy and convenient.
We learned from experience that if driving in Bath, just look for a car park that has empty spaces and pay to park. It's not worth driving around looking for a space and many of the roads are twisty, one-way city roads that are often extremely congested. Many of the sights are within walking distance to each other.
Parking in Bath is terrible.
For parking in the centre of Bath.
There is a short stay car park by waitrose supermarket.
And a longer stay one next to the bus/railway stations.
There are a couple more in the area.
For getting around it is best to take the bus.
There are also many tourist buses which take you to see all the sights.