Well being that Bit.ly is pretty much a link shortener I don't see any benefit in someone purchasing Bit.ly/E. You can always auction off your own website and with your website include the Bit.ly account (read their TOS first) but that most likely will not cause the value of your website to increase.
I don't know though, I've never done/tried anything like that before.
bit.ly is a well trusted and popular link, tons of companies uses them with their urls in order to also be able to track links and other stats. According to their website there are 20 billion bitly links already made. Having one that's only one letter is extremely rare.