Getting from Heathrow Terminal 4 to Terminal 3

Between terminals

http://www.heathrow.com/airport-guide/getting-around-heathrow/travel-between-terminals

Hotel Hoppa from terminals to hotels.
http://www.heathrow.com/file_source/Heathrow/Static/PDF/Transport_and_directions/hotel-hoppa-all-terminals.pdf

Thanks for your fast reply. Just hope I don't mess up because I didn't factor in taking a train. Oh well, we'll see this Saturday!

Just follow the signs to the train ( not the Tube). It will be labeled either Heathrow Express or Heathrow Connect which actually serves T4. This will be after baggage claim. The ride is free within Heathrow--- no ticket needed.

Thanks for pointing out what to look for/avoid. It will save me time on an already tight schedule!

There is also a free bus between these terminals - 555. It has the advantage that it arrives into the central bus station and doesn't need you to go down and up for the Hex. It isn't that frequent though, so only consider if it is close to the hour or half hour.

You can also use the underground which is free but you need an Oyster or contactless payment card to travel.

Thanks, Marco. I feel a little more confident I might make the bus to Bath on time -- now to pack for 3 weeks in a carry-on!