The best way to store asparagus is to tie it with a string or rubber band and place it upright in bunches in a cup or bowl and add a little water.
Alternatively, you can wrap a damp paper towel around the base of the bunch to help keep the stems humid and fresh for longer.
If you want to store them in the freezer, boil them in water for 1-2 minutes after cutting the ends of the stems and immediately immerse them in ice water to stop the cooking process. You can store it in a vacuum sealed plastic freezer bag in the freezer.