You need to have been to Battle Resort at least once before you can talk to all three of them. For Battle Resort to be available, you need to finish the Delta Episode.
Any Bike - Speak to a Triathlete in Battle Resort (Talking to this NPC will make others spawn)
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
P.S I'm pretty sure you need to be riding Mach bike for hex maniac and acro bike for bird keeper to even spawn, otherwise you won't even be able to get to their location anyway. If you have already spoken to any of them, that particular trainer won't be there.
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. Your second bike will be in your inventory, just like the first one, so make sure to check for it.