After you get the Forest Badge from Gardenia in the Eterna City Gym, you can enter the Team Galactic Eterna Building to rescue the Bike Shop owner.
Get a TM
Outside of the Team Galactic Eterna Building, you can go east from the building and cut the tree there to get TM46 Thief.
In the northeast corner of the building lobby, you battle two Team Galactic Grunts. You can either battle them separately talking to them from below, or battle them at the same time by walking between them.
The one on the left has a level 14 Zubat and a level 14 Glameow. You get 840 Pokédollars for winning.
The one on the right has a level 13 Wurmple and a level 13 Cascoon. You get 780 Pokédollars for winning.
After you get past them, go up the stairs.
Eterna Building 2F
If you talk to the grunt in the southwest corner of the second floor, you have to battle the grunt's level 13 Wurmple and level 13 Zubat. You get 780 Pokédollars for winning.
Talk to the second grunt from the right, and you will battle the grunt's level 15 Silcoon. You get 900 Pokédollars for winning.
After you are done there, go upstairs.
Eterna Building 3F
When you try to go to the right, you have to battle a grunt who has a level 12 Wurmple, a level 12 Silcoon, and a level 12 Zubat. You get 768 Pokédollars for winning.
When you try to go past the scientist in the northeast corner, you have to battle Scientist Travon, who has a level 15 Kadabra. You get 1020 Pokédollars for winning.
Afterward, go up the stairs.
Eterna Building 4F
At the top floor, you find the Bike Shop owner. Talk to the magenta-haired Team Galactic person and there will be a cutscene, and then a battle will begin.
Jupiter has a level 18 Zubat and a level 20 Skuntank. You get 1840 Pokédollars for winning.
Before You Get a Bike
Please note that after you get a bike, you won't be allowed to go west from Eterna City until you have gone far enough south. If you want to explore more in the west before you proceed, don't get a bike yet.
Get a Bike
After the battle, go to the Cycle Shop and talk to the owner. When you go outside, choose the color that you want for your bike. You will get to see how it looks and can say Yes if you want that color or No if you want to choose a different one.
You can press B to switch between going more quickly and improving control.
To dismount, you can go to the Key Items pocket in your bag and use the bike. You can also register the bike, which allows you to press + or - to use it.
Go to the Cycling Road
Go south from Eterna City to reach Route 206, also known as Cycling Road.