Sounds like you agreed to the new flight without any reparations. At this point they are not obligated to do anything for you as the change was voluntary.
Next time, get it in writing before you agree to anything. This goes for many things in life. I would not have boarded a plane without a paid-for car service arranged to pick you up on arrival, on JetBlue's dime of course. I strongly doubt they will pay for your rental car; if you are lucky, they may give you a $25-50 voucher which is what public transportation would have cost.
Hindsight is 20/20.
-J.