But with the GPS, I'm not sure how to
proceed. Should I just draw a straight line and file direct?

Yes. ATC doesn't care how you get there, provided you do it correctly,
as you file.

Even before GPS was ever heard of, I would file "direct" to Dulles and
DCA, ratehr than by airways, because I could do that using just VORs.
I was never asked how.

vince norris