Put a large inductance in series with the input and a large capacitor next to the circuit (on the circuit side of the inductor). Put the sense resistor between the inductor and the bench power supply and probe across the sense resistor with the scope (watch you dont short anything to ground with the ground clip of the scope). If the voltage is flat, you can then probe the voltage with a voltmeter and get 2 decimal places of accuracy.
Inductors are generally better than resistors as you dont get a large voltage drop with load
The inductor smoothes out the current and the ac current demand for the circuit comes from the capacitor