When creating a simple electromagnet, all you need is a nail and some copper wire, and a battery. I did this using non-coated copper wire, and after thinking about it for a bit, I was confused as to why it was working. Theoretically, the current moving through the coil around the nail should induce a strong magnetic field concentrated in the center of the coil (in the nail). However, if this wire is not coated, wouldn't the current simply "jump" between coils rather than following the spiral pattern around? And since it is no longer moving in a coil path, wouldn't it fail to create an electromagnet? Yet still, the electromagnet was able to pick up several paperclips with only about 20 coils around the wire.
Your bare copper wire probably has some tarnish (a.k.a some oxidation) and oil on it that may allow some of the coil turns to act like an inductor instead of being a total short.
You are on the right track though of realizing that you would not normally make an electromagnet coil out of bare copper wire. Normally enamel coated wire is used for coils because it insulates the turns but is still thin. The thin coating allows the wire turns to be packed more tightly on the coil resulting in more total turns in a given space. If you even tried to make a coil with wire insulated with thick plastic, PVC or Teflon insulation you would note the difference in the performance of the electromagnet right away.