Meaning of "Bring out the devil inside me"

Solution 1:

My sense is reflected in the colloquial devil: OED

colloquial. Fighting spirit, wildness; temper or energy that can be roused; mischievousness.

So I would interpret the phrase as:

Oh baby you allow my wild side, my energy, my mischievousness to come to light, to being, to the surface (to be brought out).