The two bikes are necessary for getting some items in a variety of areas including the Safari Zone and various Mirage Caves. To get both bikes, you need to advertise Rydel's Bikes to 3 different people throughout the region
- Mach Bike - Show the Mach Bike to a Hex Maniac in the Route 111 Desert:
- Acro Bike - Show the Acro Bike to a Bird Keeper in the Acro
Bike area of Route 119 - Requires Surf & Waterfall:
- Any Bike - Speak to a Triathlete in Battle Resort
Once you have spoken to all three of these characters, return to Rydel's Cycles in Mauville City and he will give you the other bike, so you now have both bikes at the same time.
From Pokemon ORAS Bicycles - Serebii