The Alcubierre metric is time independent, i.e. it assumes the drive has always existed in the past and will always exist in the future. It does not describe how the drive accelerates up to its cruising speed and it does not describe how the drive decelerates back to rest again.

The drive works by using a torus of exotic matter. As HDE 226868 describes in his answer this deforms spacetime in such a way that the drive moves at a constant velocity. Note that this does not require any energy to be supplied because as long as an object moves at constant speed, i.e. does not accelerate or decelerate, its kinetic energy is constant. However it does take energy to accelerate and it does take energy to slow down again. Your problem is working out how to supply the energy.

The Alcubierre metric doesn't help you here because as I mentioned it doesn't describe the acceleration or deceleration. To start the drive you would have to start with the exotic matter widely separated and you would have to bring it together to form the torus. As you did this the drive would start to accelerate. Then you'd have to separate the matter again i.e. dismantle the torus and take the pieces far away from each other. That would bring the drive to a halt.

And it's going to take energy to assemble the torus to start the drive, then it's going to take energy to dismantle the torus to stop the drive. This is your problem. Were do you get this energy? Alcubierre drives need huge masses - gigatonnes of mass. You have to figure out how to pull in this huge mass from a large separation and then push the mass back out to a large separation when you want to stop. It's not obvious that this is any easier than just accelerating a conventional drive in a conventional way. If you need superluminal speeds then you need something like the Alcubierre drive. For subluminal speeds it's not obvious that it offers any advantage.

The Alcubierre metric is time independent, i.e. it assumes the drive has always existed in the past and will always exist in the future. It does not describe how the drive accelerates up to its cruising speed and it does not describe how the drive decelerates back to rest again.

The drive works by using a torus of exotic matter. As HDE 226868 describes in his answer this deforms spacetime in such a way that the drive moves at a constant velocity. Note that this does not require any energy to be supplied because as long as an object moves at constant speed, i.e. does not accelerate or decelerate, its kinetic energy is constant. However it does take energy to accelerate and it does take energy to slow down again. Your problem is working out how to supply the energy.

The Alcubierre metric doesn't help you here because as I mentioned it doesn't describe the acceleration or deceleration. To start the drive you would have to start with the exotic matter widely separated and you would have to bring it together to form the torus. As you did this the drive would start to accelerate. Then you'd have to separate the matter again i.e. dismantle the torus and take the pieces far away from each other. That would bring the drive to a halt.

And it's going to take energy to assemble the torus to start the drive, then it's going to take energy to dismantle the torus to stop the drive. This is your problem. Were do you get this energy? Alcubierre drives need huge masses - gigatonnes of mass. You have to figure out how to pull in this huge mass from a large separation and then push the mass back out to a large separation when you want to stop. It's not obvious that this is any easier than just accelerating a conventional drive in a conventional way. If you need superluminal speeds then you need something like the Alcubierre drive. For subluminal speeds it's not obvious that it offers any advantage.

Footnote: a quick note on the masses required. Alcubierre's original drive required exotic matter with the mass of Jupiter. Various modifications of the geometry have been made to reduce the mass required, and Harold White at NASA has suggested it could be reduced, though as far as I know he has not published a proof of this. I have seen the figure of 800kg in popular science articles but I cannot find this in any of White's publications so I don't know where this figure came from. His paper Warp Field Mechanics 101 is often cited but the figure does not appear in that paper.

Chris Van Den Broeck has suggested a radically different geometry described in his paper Alcubierre’s warp drive: Problems and prospects (behind a paywall I'm afraid) that could reduce the mass required to negligible amounts. However this requires densities that are so high as to be physically unreasonable i.e. 77 orders of magnitude more dense than the matter in a neutron star.

So at the moment there are no realistic proposals for reducing the mass of exotic matter required for the drive to a figure that could be reasonably handled by a spaceship.

For completeness I should point out that all the physicists I know (including myself) do not believe that exotic matter exists so the point is moot anyway.