Hi Kevin,
You don't need a dual supply to power a transistor. A single supply with a resistive voltage divider for the base will work fine.
Why do you vary the collector voltage? The transistor circuit that you show has the transistor as a constant current sink, therefore changing the collector voltage won't change its current.
Hi Swaree,
Why do you want to measure transistors? You don't trust that new ones are good? I have seen millions of new transistors and have never seen a bad one, just new transistors that don't work because they are installed backwards.
Transistors have many paramanors (current gain, voltage limits, cutoff frequency, etc.). Which ones do you want to measure?