I took the Best of England tour last year. I was already in London when I had to go to Bath to meet the tour. This is the information RS sent regarding how to get to Bath. If you feel your arrival is too late and you don't want to go directly to Bath the same day you arrive in England, then as you said stay at a hotel the night before near Paddington Station and then go to Bath the next morning. Do arrive at least one day before the tour starts as to relax and get rest. As well as if there are any problems flying in and avoid missing the tour due to plane delays. Are you staying at Brooks Guest House? Lovely B&B and once you arrive by train into Bath, it is an easy cab ride to the hotel. I took the train from Paddington Station directly to Bath and it was easy. I bought my tkts and reserved a seat before hand. I don't know of any hotels right near Paddington Station. But I stayed at the London House Hotel which is very reasonable and it is one tube stop away from Paddington or a 10 pound cab ride to the station and a very quick cab ride which is what I did.
Option 2: Train via London’s Paddington Station ~ You can take the Heathrow Express train (www.heathrowexpress.co.uk) for about £20 (4 per hour, 15 minutes), the Heathrow Connect train (www.heathrowconnect.com) for about £9.50 (2 per hour, 30 minutes) or the Tube (subway) for about £6 (departs every couple of minutes, 50 minutes) per person to Paddington Station. From Paddington you can then take a train to Bath. Trains leave for Bath from
Paddington Station about twice per hour, and the trip takes around 90 minutes. Tickets to Bath
start around £15 when purchased in advance at: www.firstgreatwestern.co.uk. Consider this option if there are no direct buses that work well with your arrival time at London Heathrow.
Option 3: Train via Reading ~ The RailAir Link Shuttle from Heathrow Central leaves frequently for Reading (pronounced Red-ing). The trip takes around 40 minutes and tickets are about £19. See www.railair.com. From Reading catch a train to Bath. This trip takes about 1 hour, and tickets start around £13 when booked in advance. See www.firstgreatwestern.co.uk.