You can only upgrade bmi flights with miles, and since there aren't any BD flights to the US any more, that's out. For 4 people in business class, that can take a bit of creativity - you'll struggle from LHR direct, but generally LH and LX can be a good bet as long as you don't mind a detour via the continent.

What sort of time are you thinking of going? If it's the summer holidays, don't forget that a lot of the availability might already have been snapped up, as seats can be released almost a year in advance.