I wouldn't...if nothing else i'd feel a bit weird as an adult asking for an autograph.
That being said i do have some signed stuff - books, couple of signed football jerseys, a cycling jersey and a poster (the poster in particular i treasure greatly) and they are nice momentos to have. I dont "use" any of them though, they are either in frames on the wall or on the bookshelves.
A bike is a bit different though - would much rather ride it than mount it on a wall and the thing i regret on the couple of occassions when i've riden with famous pros isn't that i didnt ask for an autograph but that i didnt get a good photograph taken with me riding alongside them...that is what i'd recommend you try and get rather than a signature on a frame.