Another couple of options are Heathrow Express to Paddington and change platforms (no steps or escalators) to the half hourly service to Bristol Temple Meads.

You can also get a non express service to Paddington which stops at Hayes and Harlington. From there you can pick up a service to Reading from where you can pick up the Paddington Services to Bristol Temple Meads. Reading is a big station and since the refurb it's quite easy to change trains there.

Depending on where your meeting is in Bristol it may be easier to get the service to Bristol Parkway. Not all Paddington -Bristol trains go via Parkway but the Paddington to Cardiff / Swansea services do, so again they're half hourly ish.

Its about 1 hr 40 mins from London to Bristol, 1 hr 30 to Parkway. (picking up the service from Reading knocks about 20 mins off).

If travelling by train in the UK try to buy your tickets in advance, avoid travelling during peak time services and if you can specifiy which train you want to travel on - all of which help reduce the cost considerably.