When I was little, the kids at school used to tell me that chewing gum would stay in my stomach for eight years if I swallowed it. (I have no idea if that's true, but to this day I think about it every time I chew gum.)
Anyway, I'm not sure about the lifespan of chewing gum that gets stuck on a bicycle. But it's at least two days, unfortunately.
(Yes, I know I could remove the gum on my own. But then I'd have to get my hands dirty. And you already know how much I hate doing that.)