Having now played the demo and tried out the alternative to the bike, I have to say that I really wish biking were still an option (in addition to riding Pokemon). It seems slower to call up a Pokemon to ride than it does to quickly pick my bike option, and for breeding, that seems like it will be a pain.
I also do feel like there is value to being able to fly normally as well as a soaring-type flying option. While I ultimately went for soaring most of the time in ORAS (because I didn't like carrying a flier all the time, and because I enjoy taking in Hoenn's landscape as I fly over it), soaring is slower than the old flying menus when it comes to getting all the way across a region. There are times when I would like that speed.
I also wish you could ride your own Pokemon, rather than just calling up outside Pokemon to ride. Not sure if that will be a feature in the actual game or not (it's possible the demo just doesn't give you that option, as you don't really have any Pokemon), but I would love to surf, soar, and ride on any appropriate Pokemon that I might have.