As far as I am concerned, BSNYC has come up with the best definition of 'cyclist' I know of:

A cyclist is:
"1) a person who rides a bicycle even when he or she doesn't have to; (and)
2) a person who values the act of riding a bicycle over the tools one needs in order
to do it." (see Bike Snob pp. 44-47)

A very compact definition that says it all, in my view. The only comment I'd add: "bike rider" is, like "biker," to be applied to and only to motorcyclists.

That is all.