Question

which statement describes what most likely occurs when I Compass is placed next to a simple circuit made from Battery, a light bulb, and a wire

Answer 1

I believe the statement would be that, A magnetic field created by the electric current causes the compass needle to move. 
An electric current through a conductor creates a magnetic field,such that when a charged particle such as an electron, proton, or ion is in motion, magnetic lines of force rotate around the particle. Since current moving through the wire consists of electrons in motion, there is a magnetic field around the wire, which causes the compass needle to deflect.