In Pokémon Crystal, you get the Bicycle by talking to the owner of the Bike Shop in Goldenrod City. You can find the Bike Shop directly to the southeast of the Goldenrod Department Store.
You’ll arrive in Goldenrod after crossing Ilex Forest and clearing Azalea Town.
And you’ll be able to obtain the bicycle as soon as you reach Goldenrod.
Note: Although the Bike Shop owner says he’ll loan you the Bicycle, you’ll eventually be allowed to keep it permanently once you ride it enough.
Getting the Bicycle (Step-by-Step)
The Bike Shop’s location isn’t very intuitive at first because it’s hidden away at a dead end.
Here’s how to get there.
Step 1: From the entrance of Goldenrod City, go all the way north until you see a small street leading to the right. It’s located directly before Goldenrod’s metro tracks.
Step 2: Once you find the path leading to the right, head that way.
Step 3: Then turn south into this alley and keep going all the way down until you find a house at the end – this is the Bike Shop.
Step 4: The house with a signpost out front is the Bike Shop. This corner of Goldenrod is very small, so it’ll be easy to find it.
Step 5: Enter the Bike Shop and talk to the owner to receive your Bicycle for free.
The Bicycle allows you to move much faster, and it’s especially helpful for quickly hatching eggs you get from the Daycare.
And although Johto has no Cycling Road, you do need to be riding the bicycle to enter Cycling Road in Kanto.