If you disconnect the inflator elbow from the BC to rinse the bladder, a couple of words of caution:
1. Don't lose the o-ring or gasket that seals the connection. Scubapro, for example, has an o-ring that sits inside the female side of the fitting on many/most of their BCs. It's easy to lose when draining the bladder. To compound things, it's a non-standard size so you have to go to a dealer for another one and hope they have one in stock.
2. Be careful not to cross thread the connection when reattaching the elbow. Some BCs have fine plastic threads that are easy to wreck. If you feel resistance in the plastic threads when screwing it down, back off and start again.
3. Some wings (Dive Rite for example) have a flange on the elbow that has to seat properly in order to seal on the gasket. If you rotate the elbow a bit as you screw it down, you'll feel it click into place as it seats.
4. Whatever you do, if you remove the inflator elbow, fully inflate the BC and check it holds pressure for at least 5-10 minutes before your next dive.