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In E.T. the bicycles fly. In old films we see some inventors try to construct a bicycle which flies, with wings similar to a bird's.

Yogi bear has a flying ship.

See the picture above the site. The rider is at top of the hill. but if the bicyle could fly he could go anywhere, like Willy Wonka's elevator.

Has any flying bicycle been invented yet?

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The first human-powered, fixed-wing aircraft flew in 1961, the SUMPAC. Several other such craft were flown in the 60's and 70's, including the Gossamer Condor, which won the prestigious Kremer Prize for human-powered flight. All of these were powered by a human pedaling, like on a bicycle.

An aircraft with wings that flap like a bird's is called an Ornithopter. None that I can find were capable of getting into the air on their own. Early, unmanned ornithopters were powered by large rubber bands or gunpowder charges. The first verified human-powered ornithopter flew in 1929, but it too was towed into the air.

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Depending on what you consider a bike and what you consider flight this helicopter may qualify:

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