Remove Air Bubbles From Brake Lines

I didn't take any pictures today, but I should have.  There are a couple of small (1" or less) air bubbles that have developed in the brake lines.  We got down the oil pump can and filled it with brake fluid.  I used a large syringe to a piece of tubing and used this apparatus to draw the brake fluid from the reservoir in the engine compartment.  I attached the tubing from the oil pump to the right brake caliper bleeder valve, opened the valve and began pumping.  I was able to push the bubbles out of the right brake system.  Everything seems to be fine on the right side.  I attached the tubing to the left brake caliper and opened the bleeder valve.  I began pumping and the bubbles began to move and then disappeared.  The bubbles in the left system moved to the co-pilot left master cylinder  and entered the cylinder.  We stopped and waited.  Slowly the bubble began to come back out of the cylinder.  We tried again.  The same thing happened.  Frustrated we decided to call it a day.