How should I store beansprouts?
Looks like ehow has the best reference guide thus far to storing bean sprouts

After purchasing Bean Sprouts should be stored and washed after purchasing in growing. The article indicates that the best methods for storage are the following:


Wash them after you purchase them.



  Wash bean sprouts after purchasing or growing. Wash them in cold water to remove seed 
  coats, roots and other residue that may be present. If you are using
  them within a day, store them in the refrigerator at 40 to 45 degrees.
  Place the sprouts in a plastic bag with a wet paper towel to keep them
  moist.



Store in icy water and change the water few times a day



  You can also store sprouts in a bucket of icy water and change the
  water a few times a day. Depending on how long the sprouts were in
  transit or on the store shelf, they should last longer than when
  stored in a plastic bag.



Freeze them



  Freeze sprouts for the longest storage. Wash sprouts as described in
  Step One. Then heat one layer at a time in steam for three minutes.
  Cool right away in icy water and drain. Put the sprouts into plastic
  containers and seal.


It also mentions in the article to just grow them to provide the best freshness.

Apparently the shelf life of beansprouts should only be stored up to 3 days 

Source: http://www.ehow.com/how_6178837_preserve-bean-sprouts.html#ixzz1pAEZ12Jp