Hi! I'm Ryan! I live just a shade under 10 miles from BWI, and have driven to IAD to catch flights on numerous occasions. Usually it takes me about an hour. Hell, I've showed up at BWI for a flight, been told by the agent checking my bag that my outgoing flight was delayed and I was a guaranteed misconnect at EWR, driven to IAD (during rush hour, in the rain, even!), parked and caught a flight to my destination in order to make an early meeting the next morning.
I'm not sure where you lived before Michigan, or what experience you have driving between the two airports, but I'm going to feel like I'm on pretty safe ground when I say that I know what I'm talking about better than you do here. There is absolutely zero chance that I would ever drive to WAS so that I could take the metro+bus combo to IAD. If parking was absolutely not an option, I would drive the 2 miles to Odenton and take the MARC to start that particular journey, so comparing WAS to IAD parking is completely without a point. Depending on the circumstance I would (again, since this is a thing I've done), drive to a hotel near IAD, sleep there to get up early and catch the hotel shuttle to the airport where I board my early morning flight. You can get some cheap parking deals at the local hotels if you combine it with an overnight stay. Would I fly from BWI somewhere to catch an international flight with a domestic layover first? Perhaps. It would all boil down to timing, availability, and price. The drive to one airport over the other is completely a non-factor in the decision.
Also, spoiler alert: You don't have to pay for the Dulles Toll Road if you're catching a flight - the center lanes go directly to the terminal and are free. The outboard lanes are the only one to charge, people that use the road for other purposes pay the toll. Speaking strictly hypothetically (of course) one is also able to take the free lanes, drive through the driveway at the terminal, and then exit the airport to a local destination without paying the toll. I've definitely not done that. No, never!