I just worked this one out for myself. I was working on a timer and you could see the least significant digit of the seconds changing faintly on the display for the most significant digit. I'm not certain how your circuit is designed but I wired each segment in series, so that each segment is driven by 1 output for all displays (ie the decimal segment on every display is controlled by one output). The common annode for each display is then connected to its own output. My strategy was to activate the segments one at a time and output the given segment values for the corresponding display. In your case, I would activate the first display, turn on the top segment, then change to the second display, turn on bottom segment, and repeat. Something like this:
seg1 active
seg2 inactive
top on
bot off
seg1 inactive
seg2 active
top off
bot on
This caused bleeding for me, and I eventually realized it needs to look more like this:
seg1 active
seg2 inactive
top on
bot off
top off
bot off
seg1 inactive
seg2 active
top off
bot on
top off
bot off
So basically, you activate one display, display the required value, clear the display, then switch to the next one. Looping fast enough makes the displays look constant and the clearing of the display with every iteration prevents bleeding. Sorry this post is too late, hope it helps anyone else working on the same issue.