I've had some time to observe how to AI uses the bomb, and here are a few things I've noticed:
From the description I'm guessing that the bomb is a all rounded weapon, unlike the other three weapons, launchers, cannons and beams, which does most damage to hull, armor and shield integrity respectively
The bomb is a very long range weapon, and has a longer range than missiles, cannons and beams. In fact, it appears that the optimal range is so far out that the target should be outside of visual range when the bomb is launched (this may be because of my fairly low resolution 1280x800 screen)
Contrary to my observation in my question, the bomb is guided, though its turning radius is significantly larger than the missile’s.
The bomb detonates in two stages - first the bomb explodes on contact with the enemy ship, and at the same time releasing several explosive fragments that look like fireballs. These secondary explosions can deal more damage than the main explosion if the enemy is caught in more than one of them.
The upshot of these is that the bomb is best used against large, slow moving targets, like large hulled ships or stations. Unfortunately, these enemies can also equip counter-measures such as point defense turrets which can shoot down incoming missiles and bombs.
Another observation I made is that because of its long range and high damage, combining bombs with cloaks can make for devastating ambushes because of the cloak damage multiplier. I'll update this answer when I get my hands on the next ship that can equip bombs, the Helix.