Walk fast. The bus station serves both terminals, so there isn't, by definition, a bus that runs between the two.

Your best bet is to follow signs for the Underground - the station is midway between the two and when you reach the Underground station, follow signs for T1. By going this way, rather than overground, you will benefit from moving walkways which should make your journey faster. A small tip - use the elevator, not the escalator when going up into T1 - the escalator drops you in departures and then you need to go in the wrong direction to go up another level. Turn right out of the elevator.