From Mother Earth News
Both kinds of asparagus beetles can be easily handpicked. A beetle's instinct is to drop to the ground when it feels disturbed, so hold a container of water under the plant before gently shaking it, and the bugs will drop into the water. A sheet or newspaper or pizza box works well, too.
The best way I found to deal with asparagus beetles is to plant either tomatillos or ground cherries close by. In my garden they will go for those two and forget about the asparagus. I found out by chance. I am able to harvest asparagus and zero ground cherries. The tomatillos' production is reduced.
At the end of the season, remove all the fronds that have berries and clean up well. The beetle larvae overwinter in the red fruits.