Do I have to worry about my email address being picked up by bots when it is in the documentation of code that is in a public repository like GitHub?
Go to Github, select any project at random, and start clicking links until you get to a source file that is displayed directly in the browser.
Conclusion: it is possible for your email address in a source file posted to Github to be picked up by a bot. Whether it's likely or not is another story.
Note that the authors of jQuery UI are not squeamish about putting their email addresses up on Github.