Hotel Hoppa H56 runs from DT Heathrow to LHR Terminal 4.
The other option I used (if you have an oyster card): take one of the buses running from the stop in from of the hotel to Hounslow west underground station and from there the Piccadilly line to Terminal 4.
Timing is similar, approx 30 minutes; price is cheaper using bus+underground.
If you have luggage Hotel Hoppa H56 is the most comfortable