Ah. It's not going to be possible to size it because the bulb is then acting as a resistor essentially. Unless you know what the equivalent resistance of the circuit you're testing is, and it draws a fixed current, you aren't going to be able to cap the current; Adding a resistor (or bulb) is just going to drop the input voltage and you will probably end up having other issues
For this application you should be using a bench power supply with current limiting, not a "serial bulb" (I assume you mean a fuse, which is designed to break at a low current, however these are most typically rated for several amps, not typically in the mA range). You can set the voltage and a current limit. If the current goes beyond the limit, then the power supply will drop the voltage to keep the current below the limit or latch off. You can get a fairly cheap one for about $50-60 off of eBay, which won't be the best but is sufficient for hobby use