I've a flight from Heathrow Airport T4 at 14h:00. What is the cheapest way to get from Bradford to Heathrow Airport T4, arrival : before 12h:00?
Perhaps not the cheapest, but the easiest by far will be to fly. British Airways runs flights from Leeds-Bradford airport to Heathrow (around 1 hour, plus the time to get to the airport), and normally only charges around 60 pound for them.
Other options would include train (eg, East Coast Rail to London King's Cross and then the Tube and/or Heathrow Express to Heathrow, at least about 4 hours) or bus (eg, National Express Bradford direct to Heathrow, around 7 hours).
Alternatively you could rent a car and drive.
I would recommend checking your options on transportdirect.info and nationalrail.co.uk . transportdirect.info is very comprehensive and can search across multiple modes of transport (and it works surprisingly well).
If journey time is not an issue, there seems to be a direct coach between Bradford and Heathrow airport (found it through transportdirect). If you have luggage, this may be a particularly good option. Book the ticket in advance on nationalexpress.com. Time table is available here1. Since the journey is direct, you can catch up on sleep in the coach.
Update: transportdirect.info was shutdown, try traveline.info instead (not that good)