How do I bleed a Beckett AF Furnace? The green light keeps blinking and will not let me restart it.

The green light is a indication that the reset has been pushed to many times. I recommend you contact a contractor that does oil burner work to fix the problem.

OR you can do this and still have your original problem.

Limited Reset (Restricted Mode)
In order to limit the accumulation of unburned oil in the
combustion area, the control can only be reset three
times. The reset count returns to zero each time a call for
heat is successfully completed.
To reset from restricted mode: Press and hold the reset
button for 30 seconds. When the LED flashes twice, the

Device has reset.

As far as to bleeding you need to loosen the bleeder screw/nipple and run the unit till no more air comes out. Then close the bleeder. This may have to be done a few times or until you find out why the air is getting in the line to start with.