I don't think you can count on Jet Blue making a long series of exception to policy. All they need to do is fail to do it once on a return flight and you are screwed. Instead, there are a few clear options:
1. Leave the bike at home. Rent one at your destination.
2. Use a different airline. Check the large baggage policy before purchase. Don't rely on exceptions.
3. Package the bike, if possible, in a box that enables you to adhere to the restrictions on baggage size. Maybe a frame box, and pack the wheels separately.
4. Ship the bike by some other means (eg Bikeflights).
5. Get a folding or Rinko bike.