At the risk of giving you a whole bunch of extra work, I think the idea of passing the element's ID in as a string is a bad one; I think the library being flexible enough for a CSS selector or even an element itself would be much better.
It's also worth thinking of the DOM as a toll road: if I can travel it once (and store the reference to the other side) then I don't need to pay the toll again. By the looks of things, if I wanted to bind 2 events to an element using your library, I'd have to find the element by ID twice. It would be nicer and more efficient if I could find it ones then bind the events to the reference.
It also looks like I can only bind a single event to each element.
Your library's a good start and I like the idea of something small and simple to use rather than some of the more monstrously larger libraries, but I think it needs more work before it's ready.