Do anti-ship drones sometimes intercept enethe energy shot weapons

The Anti-Ship Drone is armed with a laser, which does damage to a single room targeted randomly by the drone. It also takes the shields down one level if it hits a shield..

The Anti-Ship Beam Drone is armed with a beam weapon, which does damage to multiple rooms along the path of the beam, but which does not affect shields at all. Instead, shields affect the beam, in that each level of shield reduces the damage of the beam. Since the Anti-Ship Beam Drone only does 1 damage per room, even a single active shield can render the Anti-Ship Beam Drone completely useless.

The Zoltan Shield will absorb bomb damage (as it blocks teleporters). This is only available on the Zoltan Cruiser ship, though.

I've found that the enemy AI tends to put their bomb weapons low on the list when prioritizing weapons, so damaging the enemy weapon system will likely take them offline. As they have low power consumption, though, it's easy for them to repair and repower.

Other than that, bombs are unique in their ability to bypass shields and drones. As you've noted, evasion helps, but otherwise there's nothing you can do but repair the damage.