You can bleed the m/c without removing it. Remove the two brake lines, install plastic ones and loop them back into the reservoir and secure with a clip, then slowly pump the brakes.
I don't like pumping the aerated fluid back into the master cylinder, if any fluid gets on your paint pour soapy water on until gone, only if left on will it damage the paint.
Seems to be a couple of problems here, if you have a good pedal before starting up and it goes away when motor starts it could be the wrong booster, the booster could be for a low vac. motor.
Re bleed as BIGSHCLUNK described, furtherest wheel from master cylinder first etc. When expelling fluid don't hold bleeder open until last drop has come out, shut it just before so air doesn't enter.
Another problem, have you replaced the front calipers? if so are they on the correct sides, that is, is the bleeder at the top and not the bottom.
After re reading your original post and you said that the pedal went down by itself when motor started and returned when engine shut off, possibly a booster problem.
A few thoughts for you to check out.