I am currently playing a survival map called SkyBlock and I removed all my grass blocks but now I need to have grass. So am I now screwed or will grass grow on the dirt field?
Grass only spreads from grass blocks. If your map contains no grass blocks, it never will (unless you place them in creative mode, or otherwise hack them in). Bonemeal will not cause dirt blocks to grow grass, they will only cause tall grass (and flowers) to grow on grass blocks.
Grass grows from other grass blocks touching it.. If you have at least one grass block on it, the grass will eventually spread.
You can get a shovel with the "Silk Touch" enchantment and go to the main land!