When Buying Asparagus,
Look for tight tips, They should look healthy and fluffy, not wilted and starting to mush.
Look for good color all the way down the stalk.
If the stalks are ugly white and tough looking starting halfway up the stalk maybe you should pass them up. There can be a few inches of tough white at the end.
Avoid asparagus that is packed in ice if you see partial frozen areas on the stalk.
My German friend said that they hit two stalks together and they should resonate a bit. If you get a dead thud, then they are probably woody and not fresh.
An asparagus bunch should be close to the same size, so that they will all will cook in
the same time.
To Store Asparagus I put them in a container that I can keep them upright and then put a loose fitting plastic wrap over them.
Here is a nice video on it.