It appears that bedridden is derived from Old English term bedrida which later morphed into bed-rid, a person who typically and regularly keeps a bed
From Folk Etymology (subtitled: verbal corruptions or words perverted in form or meaning, by false derivation or mistaken analogy) by Rev. A. Smythe Palmer, written in 1969
bedridden the passive form of this word is puzzling. As it stands it would seem to denote one that was ridden or pressed by his bed, rather than one who lay upon it—the paralytic man as he returned home with his burden, rather than as he came for cure, borne of four.
It is the A. Sax. bedrida, bedreda, or bedredda, a derivative from ridam, to ride, rest on, or press; so denotes one who habitually keeps his bed: O.Eng. “bedered-man or woman. Decumbens, clinicus, ” Prompt. Parv. (cf. bedlawyer, Decumbens, ID.). Similarly, hofrede is one who keeps his house (hof), a sick man. The form bed-rid was probably mistaken for a past partc. and then changed to bed-ridden.
Walter W. Skeet (1835-1912), author of The Concise Dictionary of English Etymology, also stated that bedridden was derived from Old English bedrida and acquired erroneously the pp suffix -en
bedridden (E.) M.E. bedreden, used in the pl. (P.PI. B. viii.85); bedrede, sing. (Ch. C. T. 7351.) Corrupted from A.S. bedrida, lit. ‘a bed-rider;’ one who can only ride on a bed, not on a horse — A.S. bed, a bed; and rid-a *, one who rides, from ridan, to ride.