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
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