One of the most iconic items in the Pokémon series is the bike. It has appeared in all the mainline games and in different forms. It once again appears in Pokémon Brilliant Diamond and Shining Pearl.
To get the bike in Pokémon Brilliant Diamond and Shining Pearl you are going to have to work for it. You will need to head to Eterna City. You will have to defeat Gardenia, the gym leader, and have the Hidden Move (HM) Cut. You will then need to head to the Galactic Building in the north part of town.
Inside, you will battle Team Galactic including Jupiter, one of its commanders. After winning this battle, the man being held captive will invite you to Rad Rickshaw's Cycle Shop. This can be found south of the city's Pokémon Center.
Here you will be able to get the bicycle and even choose between blue, red, yellow, or green. The color doesn't change any features so just choose your favorite! While riding the bike, you can press B to change gears. This will change your bike's speed and even let you go up muddy slopes.
For more information on Pokémon, check out How to get the Old, Good, and Super Rod in Pokémon Brilliant Diamond and Shining Pearl and How to make money fast in Pokémon Brilliant Diamond and Shining Pearl on Pro Game Guides.