We are arriving at Heathrow and planning on taking the bus directly to Bath. Does one need to pre-book the bus or can one just buy your ticket at Heathrow?
When are you arriving at Heathrow? And how many people?
It is possible to buy tickets at Heathrow. At quiet times it is not difficult to get a seat. However, I am not sure about busy times, and/or for a large group.
Also see my response to this other present query:> https://community.ricksteves.com/travel-forum/england/which-fare-to-buy-for-train-ticket-from-london-paddington-to-bath
There will be two of us.
My husband and I are going to travel from Heathrow to Bristol by coach in September. I was given the advice that we could just wing it and buy tickets once we arrived, but we decided that we wanted to have a reservation in place beforehand. I did pay the extra GBP5/person for the flexpass ("Change and Go" on National Express) to change coaches +/- 12 hrs in case of flight changes. So yes, we paid extra for the peace of mind and the flexibility. I think you should be okay in quieter times but not sure about the busy summertime.
Something to think about - how often are the coaches to Bath? Are you okay with having to wait for the next one, in case the one you turn up for is booked? How do you feel if you both get seats, but not together?
Have a wonderful trip!