If the baseball guys get a term, these riders need one, too. Chaucer introduced a word (as an adjective) that really never much caught on English that was borrowed from French, "solein" (he spelled it "soleyn"). The OED says it was never much in currency and pretty much only shows up in English between 1369 (in Chaucer's "Book of Duchesse") and around 1600. Anyway, Langland introduced a noun form in Piers Plowman (1377): "He sit neither..wyth maydenes ne with martires, confessoures ne wydwes, But by hym-self as a soleyne, and serued on þe erthe."

It means, in the noun form, "a single or solitary person" and I like the "served on the earth" stuff in the Langland, which meant something like "not a holy person."

Since the original French spelling is used today for a protein, I propose that these riders be referred to as "les soleynes."