It may be a compatibility thing as we didn't know about Windows 7 64 when CS3 was shipping.
One thing I might mention is that you can import folders via Premiere Pro's import command. This might be of help to you.
I'm running it in compatiblity mode for Win XP (SP3). I could try other settings to see if it helps. It's just weird, since it worked without any problems in the release candidate.
I really hope someone can come up with something that I might be doing wrong.
Yes, as I wrote in my OP, I can import items. But when I'm looking at a clip in Bridge that I want to open in PP, it is a bit inconvenient to have to do it via import. It isn't a huge deal, but drag and drop sure was a nicer way of doing it.
Thanks, Dennis, for the reply.
Can I mark my own post as a "correct answer"?
I just discovered the problem isn't PP CS3 at all.
The problem is Bridge CS4. Or, more accurately, how I am running it.
In order to do drag and drop from Bridge, it needs to be executed in "Run as administrator" mode.
So, fantastic! There is an quick, easy solution that works.