At this stage of the game, You need to pull that grass. Hopefully after a good rain. Composted manure or regular compost in the late fall When you cut the ferns. Put on at least to inches, in the spring the asparagus will push up through it. but it will hold down annual weeds both grasses and broadleaf. Exceptions are Bermuda and purple nutsedge. Those two you need to dig up the crowns this fall and restart in a different spot.
