There are 2 AP perks that will give a bonus for riding a Chocobo, called Chocobonus and Chocobump. These perks will give you AP points and EXP simply for riding a chocobo. When you purchase these perks will purchasing Chocobonus overwrite the perk to give AP points from Chocobump?
The quick answer is no. Both perks can be used together to earn EXP and AP points from riding around on a Chocobo. Both of these are best bought early on in the game to maximize the return you get from using them.