I acutally thought about this when I was asking the new cut like moves thingy. My current idea is to hijack the overworld routine(which basically takes the Overworld ID as input and then loads the sprite) so that the bike overworld is replaced by a dynamic ID. This way you don't have to concern about graphics anymore. I actually already wrote such a routine, but replaced the normal hero OW, it would not be a problem to extend this for the bike OW though. I also thought about making an item to do this job, one could basically hack the bike routine to do this and just check for any ridable pokémon in the current party. If there is no such pokémon it would basically not work and display a message. It would be way cooler though to have the ability on the pokémon itself(Like on the menu or as a dedicated move)
Everything else can be done very easily(You can see the outcome of this in the pokémon sovereign of the skies thread or on the youtube video: https://www.youtube.com/watch?v=IcYepxEgAHA
I may also give you the code sample for this if you want just ask me via PM it's for the german emerald version though (BPED) and you need to figure out the needed branches and routines yourself for your version(also the dedicated offsets)
What would be still really nice would be a way to implement this in a user friendly way. An item would be fine but how would it look like? Like a whip? Guess that would be rather harsh. Also the user can't decide which pokémon to ride this way. Not the best option I suppose...