A common misconception is that the rubber tires on a car insulate the passengers from a lightning strike. The fact of the matter is that the car body, being metal, routes the current over the surface of the car and does not enter it, then jumps to the ground. A metal cage in which current will not go into is called a Faraday cage, named after Michael Faraday, the father of electricity, as he is sometimes known as in history books.
A bicycle clearly is not a cage. Being metal it is like a lightning rod. The tires offer no insulation from a charge that can blow a hole through an inch-thick steel plate. It is possible that the strike would not go through the rider of the bike, however, it is just as likely as the current will fry the bugger to a crisp. In that case, can I have your bike?