With the first killing soon approaching, asparagus ferns will die and turn brown. Remove them at this time,leaving a small stub to identify where the plants have been growing. You can them mulch using wth bed straw and placing a 4" layer on top of the bed. Whenever manure is used ,it should be placed on the surface and allowed to decompose for at lease 6 months. Expect a few weeds in the spring,a light cultivation will prevent them from becoming established plants.