The trains turn and cross right before the Third Ave bridge and you lose your corridor. 138th street is a "painted" bike lane for what it worth and that kind of gets you over to the the Bronx connector. That's what they call that little bridge over the Kill. Randall Island is nice to ride around. There is a bridge that crosses to the East River Greenway or you can take the RFK bridge to Queens.
Crossing the Willis puts you able to connect up to the Bike lanes on 1st & 2nd ave. So if the bring it down to that area lost of connectors.