"See, see, rider..." means "Look, look, lover...."

"See" twice created parallelism with "done done." ("Done done" was an actual colloquialism.) There are many variants of the "See See Rider" family by early-born blues musicians in which the corresponding line to "see see rider" is "look here mama" or the like, and those were likely around earlier than the "see see" wording. As an example of those, Joe McCoy sang "Well look here mama, see what you done done" in "That Will Be Alright." The wording "see here mama" is in e.g. Willie Walker (born 1896). Freddy King sang "See see baby" because it doesn't matter if it's "baby" or "rider," which mean the same thing, just as it doesn't matter if it's "look" or "see," when you're in fact saying look, look, mama.