The bulb will get brighter
It doesn't matter where the bulb is in respect to the battery, as long as the circuit is complete, the bulb will light up.
Nothing special should happen. What matters for the bulb is the voltage difference between its ends.
Disconnecting a wire from a battery would break the circuit. If the battery was powering a bulb, the lamp would go out.
When the switch is turned it completes an electrical circuit. The circuit amperage flows through a high resistance filament in the bulb and it starts to glow. The bright glow from the filament and the reflector behind the bulb is what creates the flashlights beam.
Close circuit is a complete circuit of battery wire bulb and a switch
Circuit
series
You can use a circuit.
If you connect the circuit properly the bulb should light up. That means attaching the left side of the battery to the right side of the bulb using a wire and attaching the right side of the battery to the left side of the bulb. If you do that the your bulb should turn on. If it doesn't then try changing the battery or the bulb.
The whole circuit fails - because the action of the bulb blowing cuts the circuit.
Simple parts of a circuit are switches, light bulb, battery and connecting wires.
If you are talking about the light circuit then : The Battery, The bulb and the wire.