I don’t know why RS suggests that after a long flight people will feel like making their way to Bath as soon as they arrive, as it’s not as though it’s on a direct rail line.
It will take you 15-30 minutes from landing to make your way to passport control. Last month at Heathrow, non EU passport holders only got through passport control within the anticipated 45 minutes on one day. Some waited up to 2.5 hours, according to press reports this week, so unfortunately, you are unlikely to catch the 2.20 coach.
It doesn’t make sense to travel to Bath on the Saturday to travel half way back to London early Sunday morning. Stay in Salisbury on the Saturday or London and hire a car on the Sunday. Please don’t attempt to drive from London to Bath immediately upon arrival when you are jet lagged.
Most car hire offices in smaller U.K. towns do not open on a Sunday.