There's no 'fast' way to do it other than taking a cab. That'll be about 15 minutes. Using buses, you're probably looking at an hour. At least.
If DHS is open, I'd recommend taking the bus from ASM to DHS, then either walking or taking the boat to BC. DTD buses run less frequently and don't run at all in the early morning.
If you're going to BC after DHS closes, your only option is to take a bus to DTD and then grab a BC bus.