It's in Cerulean City. You get the Bike Voucher from a guy in Vermillion City,
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In Cerulean City. You have to go talk to the Pokemon Fan Club Chairman in Vermilion to get the bike voucher before you can get the bike though.
There is no bike shop. I for got where you get it from but I do have it.
The bike shop is in Eterna City.
In a shop
The Bike Shop is located in Goldenrod City.