Invictus eques seems to apply to horsemen, but I'm looking for riders in general (or particularly motorcycle riders but I'm not expecting that in Classical Latin).
Salve. Latin goes far beyond the classical period. Words such as motorbike rider exist in the contemporary Latin vocabulary.
I came across the word "vector," which means "one who rides" (Elementary Lewis) or "one who is carried" (Cassell's), in both Smith & Hall and Cassell's Latin Dictionary. From there, meanings such as "horseman" or even "motorcyclist" can be derived. A search in the Lexicon Morganianum rendered "cyclist" as "birotarius," a derivative of birota. One could, from there, add the prefix auto to form "autobirotarius," which would be a derivative of autobirota.
I think either vector, ōris m. or autobirotarius could work.
For "unvanquished," I might use "invictus" as your translation uses.
This would render the phrase as "vectōrēs invictī" or "autobirotariī invictī."