The sibling replies are mostly a load of bollocks. E-mail based publishers track clicks anyway through much better means, such as Mailchimp's click tracking - no reputable sender needs to use bit.ly to track stuff.

The reason bit.ly links can end up in mails is if third parties want to track clicks separate from the sender and the sender isn't smart enough to catch it. For example, people who want to include a job listing or some sort of sponsorship or advert in your mail. They'll often use bit.ly, simply because it works fine on Twitter, without realizing it's not a great idea in mail.