When fraternities choose their pledges during rush, a bing is someone who is between getting a bid (accepted) and a ding (rejected). In other words, a pledge wouldn't want to join a fraternity if he found out he was a bing, because the members weren't sure they wanted him (i.e. maybe they just took him because they needed to fill the last open slot). This is comparable to being the last guy left when picking teams.
Evan Blue's nickname was "bing" and he never knew why.