The spray bottle MIGHT work but it might also make the problem worse.
It's interesting how some dogs think this reverse guarding-type thing works to protect those they love, isn't it? WHAT could be going on in their little minds? "I couldn't keep that bad guy from coming in, so I'll keep him from leaving?"
Weird.
How about if you teach a down/stay? The dog can't bite if he is in a down/stay.
Alternately, using a leash is a good idea. What's more inconvenient: picking him up, leashing him, teaching him a command, or having him bite someone?