You get the bike voucher from the old man in the Pokémon Fan Club building in Vermilion City.
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To get a bike on Pokemon Yellow version, first you need to go to Vermilion city. Go into the Pokemon Fan Club and talk to the Chairman. He will give you a bike voucher, and then you can go back to Cerulean City and trade your bike voucher for a bike at the Bike Shop. (Although the bikes are offered for sale at the shop, the price shown is just over what any player can actually carry. Thus, the Bike Voucher is the only way to obtain a bicycle.)
Go to the Pokemon fan club in vermillion city and talk to everyone. One of the people give you a bike voucher. Go to cerulean city into the bike shop to get a bike with the bike voucher.
A bicycle can be obtained by receiving a bike voucher from a man in Vermilion City. This voucher can be turned into the Bike store in Cerulean City for a free bike. A bike can also be purchased in Cerulean City for 100,000 credits.
Go to Vermilion City and go inside the house above the gym which is the Pokemon Fan Club. Talk to the Chairman and listen to his story and eventually he will give you the Bike Voucher.
There is not a bike voucher in Pokemon sapphire