Certified GKH Gardening Expert
This will depend on how long it takes to dry. I would wait to water until the top two inches of soil are almost completely dry. You can check this with your finger. As far as fertilizing... You can fertilize once per year with a granular, or slow release, or every few weeks with liquid fertilizers.
Here is an article on the care of asparagus: https://www.gardeningknowhow.com/edible/vegetables/asparagus/growing-asparagus.htmhhhhh