My mother lives in the northern part of Lampasas County, about 125 miles north of San Antonio. She has an asparagus patch that she has been battling bermuda grass and some other weeds in. She has mulched it and pulled the grass and weeds and threatened to throw salt on it (some gardener off the radio suggested that is a cure but I assured it would "cure" the whole patch, asparagus and all!) I told her that there is an herbicide that can be used in an edible garden but I don't know what it is. I don't know if the weeds are broad leaf or what they are.
Salt is the old-time remedy to "cure" the weed problem because asparagus is one of the most salt tolerant of all plants. The idea is that the other plants will die from the salt but the asparagus still lingers on — alone but not NEARLY as productive. There are two modern-day techniques of grass removal from asparagus. The herbicide named Poast with fusilade kills all grasses and NOTHING else. You can spray Poast or Ortho Grass-B-Gon directly onto watermelons or petunias in which grass is growing and it will kill the grass and not damage the broad-leafed flowers or plants. Another technique in asparagus is to apply a glyphosate herbicide such as Roundup, Kleanup or Finale immediately after you stop cutting in the spring (May or June when sprouts are smaller than a pencil). As you know, when harvesting asparagus, ALL shoots - large or small - should be taken during the harvest period. When the majority of shoots are smaller than a pencil and it is time to make the final cutting, cut ALL shoots (ferns) and sprouts out of the emerging grass (probably bermuda). Then apply the glyphosate spray. The spray should kill all grass — roots and all — in about three weeks and the emerging asparagus sprouts should be fertilized and water throughout the rest of the season. This should clean the bed for you. The Poast can be used as a directed (at the grass) spray throughout the season. Mix both the Poast and the glyphosate herbicides according to label instructions.