late Old English ridere "one who rides, trooper, knight, mounted warrior," agent noun from ride (v.). Compare Middle Dutch rider, Dutch rijder, Old High German ritari, German Reiter, Old Norse riðeri; "It is uncertain how far the forms were independently developed in these languages" [OED]. As "one who is carried along on or in" (a chariot, cart, etc.), from c. 1200. Meaning "clause tacked on to a document after first draft" is from 1660s.
word-forming element meaning "quality, condition; act, power, skill; office, position; relation between," Middle English -schipe, from Old English -sciepe, Anglian -scip "state, condition of being," from Proto-Germanic *-skepi- (cognates: Old Norse -skapr, Danish -skab, Old Frisian -skip, Dutch -schap, German -schaft), from *skap- "to create, ordain, appoint," from PIE root *(s)kep-, forming words meaning "to cut, scrape, hack" (see shape (v.)). It often forms abstracts to go with corresponding concretes (friend/friendship, etc.).
<a href="https://www.etymonline.com/word/ridership">Etymology of ridership by etymonline</a>
Harper, D. (n.d.). Etymology of ridership. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/ridership