How to allow air flow to return vent in a bedroom when door is closed?

The first option is to move that return air vent if at all possible. Second option, take the bedroom door down, buy an attractive large grille cover, brass preferably, as they are lovely patterned, and have it cut to fit in the bottom of the door. As it’s in the bottom of the door, there is not that much loss of privacy. The air will pull thru the grille. But like I say, it is a second option, if moving it is not possible for you. I have seen this used in older homes.

You will probably have to put a grille cover on each side of the door,with a frame around it, because the door is probably a hollow core door. We did this to our bedroom door once. It works.

Yes - what Lana said.

yes I agree with Lana or buy doors with built in vents on the bottom.

a door vent is easiest and cheapest

Typically there is a return duct in every room, plus the hallway.

If there is wall space above the door, install grills on both sides of the wall. This way the door isn't compromised.