Ok no a blown bulb won’t inhibit the starter circuit. The service manual has some good troubleshooting tips—here’s a few things to follow up
Check the bulb—replace
Check continuity of the neutral wire circuit
Check neutral sensing switch
Check starter switch circuit
Let us know how it goes
I'm with Goober... The ignition/starting systems use the neutral switch ground to complete the circuit for the starter solenoid, so the starter button won't work until that switch finds ground. You can unplug the neutral switch and ground the wire to the motor somewhere (bypass the switch) to learn if the switch is bad and test the starter button and solenoid. Make sure the bike is not in gear though.