Can I run a sub-panel with only 3 conductors?
Plan A is NO.  An open neutral will put 120V on every grounded surface (i.e. light switch cover screws). 

Plan B is NO.  A ground fault will put 120V on every grounded surface. 

Also, plan B will fail to trip breakers in the event of a high current ground fault.  It is a terrible plan.  

If you want to do it with 3 wires, you have two options, one bad.  

Install 120V-only service.

Your 3 wires are L1 Hot, Neutral and Ground. 

Install 240V-only service.

Your 3 wires are L1 Hot, L2 Hot and Ground.   Use exclusively 240V loads (easier than it sounds) and install NEMA 6 outlets exclusively.   It is not legal to do this in residential space or other domicile (hotel rooms etc.) 

The problem with this strategy is keeping it pure. Some yutz will want to install a 120V load later, and he'll bootleg neutral which will render it unsafe the same as Plan A.  

Transformer

This only requires 2 wires, but it requires a transformer.  In this case you make the outbuilding its own main panel, with its own local grounding system.   It is electrically isolated from the supply by the transformer, so neutral is locally derived and you don't (and shouldn't) connect it to the main building's neutral/ground in any way.  

Costwise, there's a "tipping point" depending on distance, whether the cost of wire justifies the transformer.  For very long runs, there's another tipping point where "step-up" transformers make sense.   This is why Tesla won the war of the currents.