Grass doesn't just grow, it spreads. It will pass from block to block and go 1 up or 3 down per block. So build a dirt staircase from the ground to your roof, never going up more than 1 block at a time. The grass will slowly grow up from the base.
I think if I'm not mistaken you can just use bonemeal on the empty block to make it grow along with quite a few blocks of the surrounding area, but you'll also get the tall grass and flowers as well which is easily cleared out