Run a 12 volt line to the bedroom from the RV's fuse panel if it's designed to run on automotive battery power (you said it was)
Saves 300 bucks (though you might want to just in cuss)
And conversion to/from 120 volt will cost you about 10% minimum or 20% total (10 up 10 down) so direct feed is best.
Now I don't like 12 v0lt accessory outlets.. They fail too often
I use Anderson Power poles for most connections but there are even better options.
I'd like a 12 volt connection less likely to come apart. The "Flat 2" (like a flat 4 trailer conneciton) comes to mind.