"Influence" has two main connotations that "affect" doesn't.
The first is that of relation to process rather than state, so that something might affect a rock but rarely would circumstances arise where we could speak of that rock being influenced.
The second, and weaker, connotation is of emotive response being involved; this is probably the connotation that makes it feel less appropriate to use in reference to a bike's performance. (We do speak of mechanistic processes being influenced, though, especially complex ones.) -- What is the difference between "affect" and "influence"?
Would you please explain these explanations more readily? I am much too confused to differentiate between these.