What's the best way to store asparagus so that it stays fresh and crisp, rather than getting droopy?
In a cup with water. You place them straight up in a small cup with a little water. Just like you would if you were storing flowers.
You'll want to store this in your chill chest on the top most rack; to avoid any cross contamination from other possible food products (chicken, etc).
You may want to leave the rubber band on to allow it to stay tidy. If you must you can cover your asparagus cup with a zip lock bag on top.
With this method we usually can store asparagus for 5-7 days.
If you must keep them longer it maybe better to just freeze them in an air tight bag. after they're dried out.
It's best to use them the day you bought them, but this isn't always possible.
The best way of storing them is putting them in a wet towel, and putting the towel+asparagus in your refrigerator. But really, try to use them as fast as you can. I don't think they can last really long (more than two weeks) like that. If they were in the fridge for a couple of days, they can be a little bit dehydrated. Just cut off the bottom 2 mm and put them in cold water for 20-30 min.
If you will need them more than a week after you bought them, freeze them! Wash (and peel if you prefer that) them and put them in the freezer; no need to cook them first. And when you want to use them, don't thaw them, you can put them frozen in boiled water.