That´s something I´m used to too. But what dive bomber1 describes is something I haven´t seen playing for over 2 years... mostly as Japanese
Hmmm - I wonder if this is a recent change to the Game then, because I have been able to see and "depend" upon it in the pbems that I've started recently (v1.804). It's almost as good as getting two "sweeps" of an enemy base, because if I have good escorts at a base a bunch of them will escort bombers in the morning attack, then some will escort in the recons in the afternoon air phase and take care of the remaining CAP.
But then, I usually assign my escorts an enemy base as a "target" even when they are on CAP themselves so that I have a better chance to have them go with my bombers, so maybe that makes a difference...
Good luck -