Snow, 53, died Saturday of colon cancer. He gave up his White House job last year after learning that his cancer had recurred.
Bush remembered Snow both as a man of "uncommon decency and compassion" and as someone who "tried to translate my English into English."
Hundreds of people packed the two-hour service at the Basilica of the National Shrine of the Immaculate Conception. They included Vice President Dick Cheney and Karl Rove, Bush's former top political aide.
Before becoming press secretary, Snow served as a speech writer to President George H.W. Bush and became a well-known conservative commentator at Fox News.
Bush and other eulogists remembered the lighter side of Snow's life with his band, Beats Working. The president said that the group was the only one to have performed both on the South Lawn of the White House and with Jethro Tull.