I could easily imagine you getting bubbles just from the motion of the rubber grommet on the MC. This may not be a good way of identifying issues there.
That said, I've had experiences where, 'Squeeze, crack the bleeder, tighten, repeat' was not working. I found that opening the bleeder, pulling a vacuum on a line from the bleeder (I did this with a long hose and my mouth) and making sure you're fed from the fluid reservoir is the best first step. Do this on the lowest caliper first, then the next, then the MC. This gets to the point where I can bleed normally.
Try that above if you haven't tried something like that yet. Otherwise, you might have an air leak somewhere. It could be time to inspect calipers, replace crush washers, check bleed nipples, and make sure you're airtight.
Never ride faster than you can stop