As much as I like the character, we probably won't see any more of River's story because this is a family show with emphasis on adventure, action, and fun for the kids - not a romance.
One thing I've wondered: when River sees the Tenant version, she doesn't say "I haven't seen this incarnation." She says "you look so young." That hints that she either knows DT's incarnation or she sees Timelords as they see themselves (how else would one recognize another one after a regeneration?). This can't be the first time this sort of thing has been brought up...