Jerry,
I am NOT a superintendent so I am answering from the perpective of a course operator and member.
The first answer is "it depends". I would defer to your superintendent as he will truly know the specific conditions unique to your course--amount of rounds, specific micro climate, rainfall, green construction type......
Having said that at a high traffic course three core aerations are not uncommon and even with low to moderate traffic, given your location and bentgrass, I can't imagine anything less than a hollow core spring and fall aeration.
Additionally, if there is severe summer heat stress solid core venting or "needle tining" is also extremely valuable. You have to open the greens up and let them breathe for sure!
Also, topdressing is the single best practice one can encourage for smoother, faster greens. We try and "dust" our greens every week on our closed day. A light but constant application will absolutely "level out" the greens making them smoother and faster. Of course the heavy application of sand right after an aeration will slow things down but I assume you were not talking about that.
I will say that years ago our method of aerating and topressing meant we went out, pulled cores, swept them off and buried them in sand and we tried to do this all in one day. Now we start in the afternoon of a Monday (we are closed Tuesdays) to begin and re-open the course Wednesday at noon. This extra time allows us to really roll the greens and clean up the mess a lot more than just watering it in.
The green are certainly messed up but actually quite playable after the rolling. Within a day or two we will triplex the greens and after 5 days we are back to walk mowing. This saves contless reels and bed knives which would get destroyed if we mowed right after top dressing. Because of that many places won't even mow after a heavy toprdressing for days. Maybe the coursyou played had just started back mowing (though the aeration holes and sand were still quite visible)? Obviously the first cutting after the top dressing results in a pretty distinct ball speed difference even it was just a few days since mowing. Just a theory