How do I vary the range of output of a variable voltage divider
simulate this circuit &ndash; Schematic created using CircuitLab

Add series resistors on either "side" of the pot. If you want to change these parameters during use, substitute potentiometers (wired as rheostat with the wiper tied to one side) for the resistors.

These will reduce the range of the attenuation. The upper end of the range is determined by the "top" series resistance (R3) and the lower end by R2.

However, something to note:

Presumably, this circuit will be driving a load (i.e. it will be connected to something). That something has an input impedance. As drawn (and as in the circuit above), you have a 250kΩ pot as an output attenuator. This will give you a large output impedance, and so connecting to an input may give you a lot of attenuation. It is for this reason that output attenuators are typically 10k or 25k pots, rather than 250k pots. I included a load impedance in my schematic, you can simulate the circuit and adjust R4 to be a more realistic load and observe what effect it has on the output signal.

If you have a load of 10k, which is not unheard of in the audio world, your output levels will suffer, as the output impedance of the attenuator (particularly when at middle range) is far greater than the input impedance of the load.