The primary skill required for bareback riding a horse is balance. To ride bareback broncs in a rodeo, however; you need significantly more balancing 'skill' and special equipment.
The main thing is balanced. If you're a new rider I would recommend learning on a saddle first. Bareback riding can be dangerous if you don't know what you're doing.
Bareback riding requires excellent balance and the ability to stay relaxed and flexible under any circumstances. The horse will feel and respond to any physical tension you may have.