I've never understood, why it's necessary to wear running shoes to run and why someone would sell them with instructions...ok, seems legit in a game where you get a tutorial in how to use a Poke Center (with double and triple explanations that the girl on the counter can heal your Pokemon, which is exactly the same she's telling you every time)...
Back to topic: I prefer the runnng shoes, since from gen to gen the bike seems to get harder to control and I watch myself missing the doors many times in the newer games, because the bike is so hard to control sometimes. If there is some way to go, I take the bike, since it's faster.