First off, can not believe my username is allowed, I have found my people!
We moved out of Bath (camden) as the traffic and fumes are such a nightmare in town and driving out through all the tourist traffic at the weekends was driving us insane, we are about 4/5 miles out. Kingsdown, and have had no issue on the school run to Kingswood daily, we find being within sight of town but far enough away suits us perfectly, but we do a lot of outdoorsy stuff so were always in and out of town. There are many around us, Monkton Farleigh, Ashley, Atworth, Bathford, Batheaston etc at Bath schools.
It is also worth noting the canal towpath is very accessible from Bathford/hampton/easton and takes no time at all on a bike to get into town, we do this regularly from us but we have the hill to climb up so less of an easy route. There is a train from BOA to Bath every 30 mins, and again on the cycle route/ towpath.
Buses are easier if you are on the London road route so Corsham-Box-Bathford-Batheaston
Also you can get a year pass for the tollbridge if you were going to Kes every day this would be by far the easiest, friends do this, BOA, brassknocker hill, drop off at the Paragon, over to Kes then tollbridge and home, in time for work so not as terrible as you may think.
Beautiful area, you will love it