I am using 6 1.5v AA batteries to power the stepper motor. The 6 batteries are only used to power the stepper motor. This is how I wired everything up:
The motor is normally rated at 5V and 70 ohms, so each winding will take 70mA with one
winding active, 140mA with two (some step patterns like full-wave do this).
At 9V supply those values will be 130mA and 260mA instead, and you will overdrive the motor.
The first thing to do is use just 3 or 4 batteries, not 6, for the motor, that will extend life by a
factor of two-ish.
Secondly find out which step pattern is being used and change to wave drive if not already,
which is the least power-hungry.
Stepper motors are never a good choice for battery power, they take lots of power even
when stationary.
The 28BYJ-48 is a very highly geared and its almost impossible to drive it backwards (without damaging the gears), if driven in single-step mode it is possible to use pulsed drive which massively reduces the average current requirement as they don't have to be driven when stationary.
For applications that just run for a brief time to set a position 9V should work very well, especially if some adjustments are very small and plenty of torque is needed.