You can get both bikes in ORAS! This can only be done after the league though.
In order to do this, you will need to be on the Mach Bike and talk to the Hex Maniac in the Route 111 desert. Then, while your on the Acro Bike, go to the Bird Keeper in the Acro Bike area in Route 119 that requires Surf and Waterfall. Then, with any bike, go to the Triathlete in the Battle Resort.
After you've talked to these people on the respective bikes, return to Rydel and he will give you the bike you don't own.
Pics of these people's locations are available in the source, apart from the Triathlete.
Hope I helped. :)