So it seems you'll need either solid wall anchors (rawl plugs) or hollow wall anchors but you won't know until you drill. And you'llm almose definitely need the 2x4, except if it's a solid wall and you have the right expanding anchor to match your hook.

The reason for the 2x4 is two fold. One it'll reduce the jiggle on when the bike is mounted and removed which may eventually loosen the hook, and it nicely spreads the load cutting the chance of an anchor pulling out.

As far as the effect on the wheel touching the wall goes, either mount the hook as near to the center as possible while still allowing clearance below, or lengthen the 2x4 to extend to where the wheel touches the wall.