There is no way you can exchange Poke Miles for Battle Points.
As for quick ways to earn them, teach your Pokemon powerful moves that cover many types and look up the Battle Maison's leader's teams here. You can also go to the Battle Institute and try to get the highest score for more BP. The point system is on the link.
According to this, the types of moves you need to learn to have the most coverage are:
Ice, Ground, Fighting and Dark
Ice, Ground, Fighting and Grass
Ice, Ground, Fighting and Flying