You do not need a car in Bath - in fact, it would be a hindrance. Most of the main sights are easily walkable.
You can get from Bristol Airport to Bath by bus:>https://www.bristolairport.co.uk/to-and-from-the-airport/bus-and-coach
However, you may not like to pre-book as you will not be sure when you will exactly leave the airport. You will find a regular bus service outside the terminal building that is a shuttle service to the moon rail station in Bristol = Temple Meads. You can certainly by a bus ticket off the driver to get to Temple Meads. It is also possible that he/she may be able to sell you a combined bus/train ticket to Bath. If not, simply walk into Bristol Temple Meads station & buy a one way ticket to Bath. It is only a 15 minute trip and the trains are roughly at 15 minute intervals.
Best to hire a car when done with Bath & heading for The Cotswolds.
https://www.google.co.uk/maps/@51.3820551,-2.3626602,1483m/data=!3m1!1e3!5m1!1e1