40'F is pretty good at hindering mold & bacteria normal growth rates. Water change 1-3 days. Optional concentrate lemon juice to acidulate the water is a wonderful preservative. I do a similar thing for celery stalks, bok choy, lettuce heads, baby carrots, etc -- but not asparagus.

Areas of ambient high humidity would be factor for increased bacteria rates also. A water tray may not even be necessary. Dry climates will benefit more.