As I understand it the electric bill is calculated against consumption of Watts. So if your heater consumes 1500 Watts an hour your bill could be a little lower using 240v over 110v.
!!NO!! Sorry, not true. If this WERE true, then it means your wiring is seriously undersized, and that you are headed for a house fire.
Wattage for electric heat (resistive) is a simple calculation of amps x voltage. If there were any significant loss due to wiring (otherwise know as " I squared R") then your wiring is in BIG trouble.