Stansted to BHD irrespective of which runway is used would be quickest via a Compton SID, then direct SAM direct BHD.
Depending on the level that you're filing for the cruise you could end up routeing below controlled airspace west of SAM because the base level is quite high. However, most traffic is transferred to London Military west of SAM if it's staying below.
A longer route would still be via a Compton SID, but then CPT direct BCN direct BHD and unless you're flying below FL80 you'll be in controlled airspace almost all the way.
From Luton and Northolt the routeing is the same.
