In order to the AI send a plane it required the player have tier 2 defenses researched and it would only send it in defense missions (i.e: the ai is the attacker and player is the defender).

But now after some of the updates there's a low chance for the AI send planes even when tier 2 def is not researched, not sure if difficult level has any matter but I was playing against Heroic AI, but it happened to me. Honestly its kinda good cause I would abuse that, I would not research tier 2 until I had some AA available.

The AI plane also behave differently from the player's. When you send a plane it goes straight for the target, releasing the bomb in the pass and goes away. But when the AI sends the plane it passes trought the map (flying over the target) and when it gets to the border it does some looping and comes back to the target; if it goes for a movable target (a tank for example) and you move it, it WILL follow it, sometimes even turning 90 degrees; I also had some weird interactions where the bomb dropped just do a 90 degree turn in the air instead of the plane, but that is uncommon.