The Scottish Rite came into being with the formation of the Mother Supreme Council in May 1801.
I believe the York Rite was officially founded in the late 1700's.
Ancient Arabic Order of the Nobles of the Mystic Shrine (Shriners, or now Shriners International) was founded in 1870.
George Washington died December 14th, 1799.
So he was not a Shriner for sure. If I do have the date correct, and I believe I do. He was not Scottish Rite. York could be a possibility.
Now all that being said. The degrees may have well been performed in regular Lodges before the founding of the bodies. There are records of many different degrees done by some Lodges in our early history. Could he have attended those degrees? It is a possibility.
Side note, as you did not mention which bodies, I picked the top 3 in America.