how long does it take to regenrate from empty to full?

Like a few minutes

 

RS WIKIA:

Like the special attacks of a weapon, the special moves energy bar will naturally recharge over time. It does so at a faster rate of 15 points per every 30 seconds versus 10% per every 30 seconds for the special attacks bar. However, an important difference is that each time the familiar uses a special move, the recharge clock resets and another 30 seconds will pass before 15 points are restored to the energy bar.