If you add a resistor in series, then B+ will drop. The amount is determined by current flow through the resistor. You can calculate PS current draw by measuring the voltage across the resistor that's already in the circuit and using Ohms law to calculate current. Then use Ohm's law to calculate the amount of voltage drop that wil be caused by putting another resistor in the line.Ohms law is pretty simple stuff:
E = I ยท R
I = E / R
R = E / I
Where E is volts, I is amps and R is ohms.