Running out of fluid in the bleeder will not introduce air into the lines UNLESS you also let the reservoir get low on fluid.

I use a Motive bleeder for flushing brakes, but I've never used it for bleeding brakes after the system has been opened. In that case I use the two man system. Depending on the person at the pedal, you may even have to do it with the engine running. If you do run the engine, set the ebrake, block the wheels and have a brake pumper that you can trust. This is not the time to use an 8 year old.