Pokémon Brilliant Diamond & Shining Pearl: How to Get Bike

In order to get the bike in Pokémon Brilliant Diamond and Shining Pearl you will need to make your way to Eterna City:

Once in Eterna City defeat the Gym Leader and head up to the building with the three cut-able trees in front of it, north of the Pokémon Center. Once in front of the building, a cutscene will trigger where you meet Cynthia for the first time and she will give you TMs for Cut and add it to your HM App. Use this to cut one of the trees in front of the building directly above you and head inside. This is Team Galactic’s Headquarters. Head up to the 4th floor and you will have to confront the Commander, Juniper.

After defeating her speak to the man she was facing, this is the Cycle Shop owner. He will thank you for saving his Pokémon and ask that you meet him at his shop. Leave the building and head to the Cycle Shop which is located just south of the Pokémon Center in Eterna City:

Once inside simply speak to the man at the counter and he will thank you again and walk you outside. Once outside he will ask you to choose a color for your bike. Once you obtain the bike you will be informed that unlike the original you won’t have to keep swapping out your bike but instead can shift gears using   :

That’s all there is to it, now you have your bicycle.