Kathy,
Our asparagus is in a kind of raised bed. We tilled the area; shoveled out a path around the bed, tossing the soil onto the area to be planted; then put in the crowns. The area that contains the asparagus is about 6" higher than the path and surrounding area. So far it has worked well for us, even though we don't have a containing wall of any sort. Our soil is basically clay, but we amended with compost and composted manure.
From what I have learned, asparagus crowns rot if they are in wet/moist soil constantly. It sounds like you are on the right track with a raised bed to compensate for the high water table.

That's how ours are planted... Only second year, but they all seem happy and have begun producing a few decent spears. We too use lots of composted manure (and bunny poo)!
Happy gardening!