It depends what part of London you`re living in, but certain bus routes to LHR run very early end late or run 24 hours a day. eg 140, 111, 285, U3
See London Transport website
Living further out tends to be easiler to commute to LHR eg Herts, Beds, Bucks.
National Express coaches run through out the day and night and the BAA offer airport staff a discounted season ticket.
Think there site is airport commuter.
Also living on the Euston rail line and Marylebone rail line, connects to 140 bus at Harrow to LHR.
Central area served very frequently to Compass Centre. You just need to know service numbers and times. Bus 75 76 50 First Bus. London Transport 105 U3.
Move to T5 National Express will be running direct there.