You could use an opamp...one with common mode input down to 0v like the LM358.
You can google voltage regulator circuits, because they are pretty similar to constant current regulators, only instead of comparing the output voltage to a reference (precision voltage reference) you compare the voltage across a series resistor to the reference.
For low loads, the resistor can be quite high, then its just a question of V=IR. 20ma, through a 100ohm resistor will have 2 volts across it.
I guess it depends on the maximum voltage output for your constant current source, and I assume you want to vary the output via a potentiometer?
google 'low side current sensing' or 'high side current sensing'. I'm sure you'll find some pretty good circuits. Of course others have mentioned many other methods, so I didn't go into detail about using a few transistors. With an opamp and precision voltage reference, you'll have a pretty accurate current source.
Blueteeth