Actually Linda you will use slightly more fuel with the tow bar fitted, aerodynamics aside, you've increased the unladen (kerbside) weight of the car by the weight of the tow bar.
But don't worry the increase in fuel consumption will be so miniscule that under normall driving conditions you'll not notice any difference at all!
Any additional weight in, or on, a vehicle will increase it's fuel consumption. A towbar will make a slight difference but less than the effect of an extra passenger.
A difference, yes, but not enough to measure outside a laboratory.