I'm going to expand on Renan's answer because I don't think he's fleshed out all the implications.
In a nutshell: If you have an Alcubierre Drive you also have a perfect deflector for any energy or kinetic based attack. The ONLY means of attacking a ship with an Alcubierre Drive would be to ram or grapple it with another ship with an Alcubierre Drive.
The A-drive works by warping space itself, any matter or energy entering the warp follows the lines of the warp just as it were flat space but goes around the ship and comes out with more or less the same trajectory it went in with. Used defensively, an A-drive wrap field can deflect ANY energy or kinetic matter attack. Even detonating massive nukes against the warp would be pointless as all the radiation and plasma would just flow harmlessly around the ship.
The only way to defeat a space warping field would be to use another space warping field to counter-act the first field which would allow attacks to go through, although the warp itself would likely be the more effective and dangerous weapon, which would turn it into a space "ram" for thematic purposes. Even better in my opinion, it would make boarding actions possible again.
Expanded answer i.e.TL;DR (unless you have a free weekend)
An A-drive works by creating a gravity well in front of the ship, basically a gravitational simulation of high gravity object like a black hole, which the ship "falls" into but since the ship generates and moves the gravity well, it keeps falling until the drive is turned off. Creating a reversed gravity well, essentially a hill, behind the ship makes it go even faster (helps the math somehow as well.) By putting wells around the ship to make tunnels, the interstellar gasses and radiation get routed around the ship.
Since technically, it's the space that moves and not the ship, relativity does not apply e.g. no time dilation, the ship doesn't go E=MC^2 and become a planet cracking bomb, it plow up a plasma shockwave that can sterilize an entire planetary system etc.
By bending space itself, the ship can deflect or reroute any type of attack. Directed energy weapons can just be bent around the ship. By creating gravity shears, any material weapon can be destroyed and the debris routed around the ship. Gigaton nuke? Same answer, the plasma and radiation will follow the bent space and never touch the ship.
(As a bonus, the warp field can act like a cloaking device making the ship hard to detect as all light and other forms of radiation bend around the ship. Probably leave a detectable ripple of light or particles that get bent around the ship but come out with altered trajectories. But you won't be fighting in a fish bowl wherein a ship can be detect light hours away just by infrared. In a planetary system, the ripple would be even harder to detect. Cloaking allows for ambushes, sneaking past sentinels, submarine vs destroyer scenarios etc)
An A-drive makes a ship invulnerable to weapons save another contending warp field. The only way to attack an A-drive ship (Ship-X), would be to use another ship's (Z-ship), A-drive to "unwarp" the space around ship-X so that an attack could get through. "Ramming" would actually be projecting Z-ship's warp through ship-x's warp. Once through, Z-ship could warp the space inside ship-X and rip it apart.
(In the classical era, ramming developed as a tactic pretty much for the same reason i.e. no ship borne weapon of the age could seriously damage another ship, and grappling put attacker and defender on equal footing, so turning the entire ship into a weapon was the only option. Note that as ships got larger and stronger, ramming by oar powered ships stopped working. In the Byzantine era, ramming the hull no longer worked so the Byzantine dromon ship's had rams used for scraping down the side of an enemy galley and destroying their oars. Conversely, in the early ironclad era, ships guns could just barely penetrate enemy armor, or so it was thought, so ramming came back for a while, until the torpedo.)
But unless the Z-ship has a much more powerful warp, ramming would be dangerous. The Z-ship places itself in danger of being warp rammed itself during the attack. (Ships in space, especially those with a warp drive, can spin on any axis fairly quickly. It's not like ships on the water or even aircraft as they have no medium to push against. It's possible the warp field itself can be positioned arbitrarily around the ship in any configuration without changing the orientation of the ship at all.)
Also, as the two warp fields merge, with each ship constantly altering its own field to try to penetrate the other (kinda like gravity fencing) they will likely create an utterly chaotic gravity field between the ships which will itself prevent a single piercing warp from hitting the other.
Instead, the attacking Z-ship, will not try to stab a warp through but will adopt a purely defensive shield arraignment and try to merge its warp field with ship-Xs warp such that both ships end up inside the same bubble of flat space and both standing still relative to the other.
Of course, at this point, powerful ranged weapons become suicidal, it would be like fighting with AK-47s in a broom closet. Instead, time for knife work. Z-ship has to attack ship-X with a small scale weapon whose collateral effects won't be severe enough to wreck Z-ship itself.
So... prepare to repel boarders!
The most precise and lowest energy attack would be to board the target ship, defeat or avoid any anti-boarding defenses, cut inside the ship and take control.
Now you have a plausible scenario that replicates the romance of the Age of Sail. Maneuvering in interstellar space would be like maneuvering in open ocean and maneuvering inside a star's planetary system would induce all kinds of gravity complications, as happened with sailing ships maneuvering near the shore.
A fight would go something like: Z-ship detects the ripple of ship-X and moves to intercept. Ship-X might be largely blind if heavily cloaked because its warping all the light around it (like a sub without sonar.) However, when Z-ship gets close enough that the warp fields touch, ship-X will know its under attack. (One twist might be that exactly what class of ship a clocked ship is might be very hard to determine. A "destroyer" might end up attacking a "battleship.")
Z-ship distorts ship-X's warp (spilling the sails in old days) bringing the ship to stop relative or at least slowing it down. The the ships start "fencing" with their warps trying to damage or destroy the other ship at the far range of their warps but this will seldom work unless one ship is much more powerful than the other.
Z-ship then concentrates on simply pushing itself through ship-X's field until the ships are so close the warps become useless or to self-dangerous. Now the ships have to either engage with low power weapons, essentially trying to peck each other to death, or they attack with boarders.
(Boarders might be more plausible if the chaotic warp field remains at lower power between but not on or inside either ship but is strong enough to randomize the trajectory of any directed energy attacks or small kinetic attacks. As well, warp fields might be used internally to brace material components making lower power attacks less effective. If ship-X self-destructed, its warp would collapse instantly leaving Z-ship's field suddenly unopposed and able to deflect any blast effects automatically.)
If the warp fields could be generated/projected and then manipulated at the human scale, then boarders would be in same situation as ships i.e. energy and kinetic weapons wouldn't be effective against them, they could only be fought with another warp field. At the human scale and close range, this would be a return to melee fighting. Weapons would be warp manipulators and would likely take forms similar to weapons of the pre-gundpowder age. Although, I wouldn't recommend holding such a weapon in one's teeth while you board the enemy ship.
For fans of the Battlestar Galactica, aircraft-carrier-in-space scenarios: Small warp fields would also allow for small aircraft-like fighters that also can only be attacked by other warp fields. They would fight each other more like dueling raptor birds, at close range slashing at each other's fields. Against larger ships, their function would be to slash at the ship's warp field, slowing it down and randomizing its field to enable the attack by the main ship.
Stationary installations could have a warp dome over them but projecting the warp field into solid ground might be to destructive, energy intensive, randomize the warp field etc, so you could scenarios in which the ground installation, either in vacuum or atmosphere, where invulnerable to air attack but would always have a gap around the bottom edge where ground forces could slip under the dome. Again, big melee fight until the attacks reached the warp projector and shut it down. This would be akin to the Age of Sail fortress high up on a sea cliff that ships couldn't hit, so they land ground forces to take in reverse.
I think the Alcubierre Drive space warping opens ups a lot human scale drama potential while requiring only the one "magic wand" of the drive itself.