Bikes

There are two bikes in the game, each with its own special function. You can get these bikes from Rydel's Shop in Mauville City. You can only take one bike at a time; to switch bikes, you have to go back to the shop and swap it there. However, Pokemon OR/AS will allow players to keep the two bikes. These are required to traverse specific locations in the game. To do this, you have to advertise Rydel's shop by speaking with three different NPCs hanging around in different locations in the game.

• Hex Maniac: She's located in Route 111. Show the Mach Bike to her.
• Bird Keeper: In Route 119, there's an area where you can use the Acro Bike. Look for and speak to the Bird Keeper NPC while you're riding the Acro Bike. This area may require Surf and Waterfall.
• Triathlete: This NPC is found in the Battle Resort. Talk to him while using any bike.

After speaking to the three of them, return to Rydel's Shop and talk to the owner. He'll give you the other bike as a reward for your effort.

Acro Bike

Acro Bike is faster over running but its speed is not it's main feature. The Acro Bike allows you to perform "technical" stunts like being able to do wheelies (press B while moving), hop on adjacent but separate ledges, or bounce (hold B button while stationary). This bike allows you to reach certain areas that you can't possibly reach using other methods.

Mach Bike

The Mach Bike can make you move twice the normal speed. It can also go up the slippery and steep slopes where you'll normally slide back down when trying to traverse it on foot or using an Acro Bike.

Image Source: Official Site

Additional Reference: Serebii