First drop the plastic vent trim piece in the bedroom and look to see is it's pre wired. If it is it will be easy to move... If not see my earlier post about installing a 2nd AC with 30 amp service for tips on wiring a new unit. In my post we ran the romex to an exterior Marinco inlet, with 50 amp service you could run it directly to the electrical panel.
If you'll carefully roll the lap sealant off the top metal trim piece on the vent and remove the screws, you should be able to re install and re seal the same vent in the opening after you move the AC. The garage AC is held in place by four lag bolts that screw up from the lower unit and tighten it down to a compression seal. If you switch from duct-ed to non duct-ed or take it off the house thermostat you'll probably need to change the lower unit @ about $100.
If you're going to have guest stay overnight in the garage you'll need to keep an AC back there, but if you just use it to haul then moving the AC is an option. I would add a third High Efficiency (10 amp) AC to the bedroom with an inlet to plug directly to the park pedestal or to plug into your exterior GFI outlet when on the generator. The generator is only going to run 2 AC's, but with the inlet you could control which two.
To quote Ron White... "I know, I've seen me do it."
Good luck with your project!!!