I am finishing a bathroom in my basesment. The tub surround has a rough edge I need to put the sheetrock against. How do I tie these two items together?

You want to over lap the sheetrock over that lip. Cut or rasp the back side of the sheetrock so it doesn't bulge out over the lip.

You should probably just rest the sheetrock on top of that lip, so that any water that gets behind your tile doesn't wick up and wet the sheet rock. You probably shouldn't be installing sheetrock in a bathtub area, unless its dens-shield, and even then if the water wicks up behind your tile, it can still deterioate.

If the tub has a shower, sheetrock is no longer up to code unless you are using an applied waterproofing like Redguard. Otherwise, you must use a water-impervious material like cement backer board. Hardibacker, sold at Home Depot and others, is the easiest to work with. There should also be a vapor barrier behind the backer board, something like six mil poly sheeting. The sheeting overlaps the tub flange and the board clears the flange by about a quarter inch. This joint is then caulked with 100% silicone. After tiling, the tile-tub joint is also sealed with silicone.

You do not tie them together. After careful fitting , fasten the rock into the stud about six inches away from the fixture edge.
Sheetrock only needs fastening every sixteen inches or so. A well fitted board and fixture will work fine.
Don't sink the screw heads below the paper surface. Adjust your technique / tool to slightly dimple the finish sheetrock paper.