This is a great question because typically, most actors don't really know how many shots a headshot session will get them, or how many they will need to have.
I'll start by saying that you only need one great headshot to break into the entertainment industry. But I'll expand on that by saying that you should ideally have at least two great headshots, one serious and one smiling. This means one theatrical and one commercial.
Based on the skill of your headshot photographer, you need to understand that you may need more or less shots. Typically, a novice headshot photographer will be trigger happy and will continuously shoot hundreds of shots and you'll walk out of your session with 700 or 800 shots, something that can be quite overwhelming to say the least, especially since out of those, every ten will look almost exactly the same. So really, you'll be looking at 70 or 80 different shots, of which you'll probably find 20 or 30 decent ones, and only 2 or 3 very good ones.
Now on the other hand, shooting with an experienced photographer may yield you with a lower number of actual shots but many more will be useable. For instance, someone like me would give you a disk with about three or four hundred shots during a three hour session, and you'll find 200 of them good, and maybe 75 very good ones, and about ten to twenty great ones.
If you shot with someone like Peter Hurley, who charges $1,100 for a session, you may get a disk of only 200 images but 150 will be very good and 50 will be great.
I recommend that you don't worry about how many shots you are getting but rather how many useable headshots you need. You should base your decision on the number of looks you'd like, so if you want two or three looks, you might need two hours. If you want less, then only an hour is probably necessary.
Think about how many shots you need in terms of looks and you'll be able to figure out how long the session should be.