Register or return vent; Which can I block with my bed?

You don't specify if your vents are wall or floor mounted, and if the return vent serves just your room or multiple rooms (which would be unusual for a bedroom vent.)

If you have floor vents, put the bed anywhere you want, you might find the room more comfortable if you put a deflector on the supply to point the heat toward the center of the room.

If you have wall units I would put the bed near the return, but would leave the bed a couple of inches from the wall. Blocking it doesn't just stop air from getting to the furnace, it also would pressurize your room, not allowing warm air to enter.

Register.