Inflate the BCD (Buoyancy Control Device) and empty out any water from the bladder. Generally turn it over so the elephant's trunk is lowest and press the deflate button. Then hang it up over the bath / shower. Most of the BCD materials aren't that porous, so there's not that much water caught up in the material.
At the end of the day, the moisture needs to get out of the BCD and into the surrounding air. A typical home will be pretty dry, and a BCD is quite small. So, hang it up over the bath / shower, and leave the door open so any moisture (not a lot) can get out of the bathroom.
If you've a large soggy item, e.g. wetsuit or neoprene drysuit, then it can be helpful to point a desk fan at it whilst it hangs up to stir the air around a bit. Not too close, but enough to move the air over the item. Again, leave the door open to vent into the rest of your home. There's not much damp from these items, so it's not going to make anything damp.
I'm fortunate enough to have a garage and I just hang up my drysuit, regulators, inflated SMBs and (wing) BCD which dries naturally in a couple or three days (even in the winter). Only the hood takes time to dry. I hang my undersuit and undergloves (drygloves) indoors to air.