Congrats on your first camping trip!
I've used the heater in my camper with no difficulties and we mostly camp off grid (boondock). There is no problem at all running the heater with the bed set up. It sounds like you have the same bed as me - a king sized platform in a 17 ft trailer. Yes, the warm air vents are under the ends of the platform, but the air is warm, not hot enough to start a fire.
The heater DOES use battery power, for the blower. It's about the same drain, I think as the OEM fan in the ceiling draws. We just use the heater to keep the chill off, not to heat the trailer to, say 70 degrees. So, the fan does not run too much. I've reduced the electrical draws in our trailer by replacing all lights with LEDs, and I replaced the ceiling fan with a FanTasticFan. I also have two batteries installed, in parallel, which gives twice the capacity.
Hi-Lo 1707T - Tire Minder TPMS on Tow Vehicle and Trailer, 300W Solar Battery Charger, Equal-i-zer WDH
2014 F150 Platinum 4x4 3.5L EcoBoost SCrew