If you have to go back to T1 in the morning, particularly for an early flight, you'd be far better staying at one of the many hotels on the Bath Road - from all chains.
At that time of night, the paid Hoppa buses may well have stopped running, but it's much quicker to take a standard (public transport) bus anyway, which is free for most of the hotels along the Bath Road (as far as the Harlington Corner stop). Numbers 105, 111, 140, 285 from the Central Bus Station - close to T3 - will work for the hotels East of the airport (the majority are there). Many of those services run 24 hours.
In the morning, you'll find they run the other way every few minutes - add in N9 service as well. Just beware that it's more complicated if you stay in the Holiday Inn closest to the airport (the Sipson Way one) because only the U3 bus goes back, and it doesn't run as frequently. The HI Ariel is a better choice, even though it's further out.
Even the furthest hotel is no more than a 10 minute bus ride. Hoppa will generally be double that because of multiple hotel stops.