What would be good to plant within my asparagus bed?
I need more info to give an answer to that. Practically anything can be grown with asparagus. I have garlic, onions, broccoli, peppers, sweet potatoes, and lettuce growing in the same raised bed. Last year I also had carrots and flowering plants growing adjacent to the asparagus.
Eggplant did well beside my asparagus, but daughter doesnt like asparagus except for the ferns, chuckle, so did basil, and oregano
Check out companion planting. This'll tell you the best thing to grow. I grew certain herbs, and some marigolds (French type) as a result. It is VERY interesting to grow things this way. Oh, it is also quite addictive.