If you're not bothered by cost, there are plenty of taxi's available at Bromley South. The 320 bus stops at the main terminal and by the flying schools so you'd still have quite a walk to get to the hangars.
If you're driving I would go either A2 - A20 and then through Bromley or A23 - A232 through Croydon. Neither route is particularly good, but they are better then using the A21 or the south circular due to all the choke points like Catford!