Surprised that the ticket price from Washington to BWI has dropped since I bought my ticket. Only a dollar but still, I thought Amtrak prices only went up as the date approached? This is the web only "Saver Fare," dropped from $12 to $11.

Yes it has been that way for many years. Amtrak is having a 30% off sale now through Monday (President's Day).
To look at a range of dates for Amtrak trips, check AmSnag.
http://biketrain.net/amsnag/amSnag.php
Many years ago, my DW dropped me off in Baltimore to get to BWI. The fare was $5 bought an hour before the train.

Is it just the saver fares that vary, or all of the fare categories?

All coach seat categories. The sleeper fares are coach fare times the number of passengers plus the "room fee".
They sell only so many "saver" fares in coach so if you see one available, buy it right then.
The "Business" class seats look very comfy. We will be paying extra to sit in them overnight from Chicago to Erie this May.

That's news to me, I've never seen fares go down, it's basically like an airline, of course, or any train system. Usually fares go up as the best deals get sold out. Of course I never take it just to BWI from DC.

If you're going to BWI from Union Station, you may wish to see if there's a MARC train going at the desired time...in my recollection, considerably cheaper than Amtrak.

I'm going to the March for Science and need to catch a flight out that evening after the protest. I was concerned that ordinary transit would be swamped and I'd miss the flight. Amtrak guarantees me a seat. Also, can only store bags at Union Station with an Amtrak ticket. BTW: MARC train is $7.