I think a lot of folks take "cyclist" to also include "bicycle enthusiast," which while appropriate, doesn't cover the full gamut of cycling. So I'd say a cyclist is one who rides a bike.

(of course, I won't feel comfortable calling myself a 'cyclist' until I complete my first century. Until then, I say I like to ride bikes. To me, 'cyclist' in that context is the same as 'runner.' I wouldn't call myself a 'runner' unless I'd done a marathon)