I saw a photo of Air Force One and the doomsday plane together on 9/11. Did it follow Bush around that day?
No. On 9/11, the Secret Service (and everyone in government other than George W. Bush) didn't want President Bush to return to Washington too quickly because there were still a lot of questions about what was happening. After the attacks happened while Bush was at the school in Sarasota, Florida, they flew to Barksdale Air Force Base in Louisiana. But they still didn't feel totally safe because the FAA still hadn't completely grounded every commercial flight in the country yet, so the Secret Service wanted to move the President to an underground location that was capable of handling secure communications. Remember, this was 2001, so the communication technology wasn't as advanced as it is today, and one of the big lessons of September 11th was that there were some significant issues with communications aboard Air Force One. The passengers flying aboard Air Force One on September 11th couldn't even see the coverage of the terrorist attacks that everyone else around the world was watching on television all day unless the plane was flying near a major city.
They took the President to Offutt Air Force Base outside of Omaha, Nebraska because it was a safe distance from Washington and had secure video conference technology underground where Bush could communicate with Vice President Cheney and the rest of the government. Offutt just happens to be the place where the "Doomsday planes" are stationed (there's always one of the "Doomsday" planes on the tarmac at Offutt on alert and ready to take off in case of an emergency). Bush wasn't actually at Offutt for too long because he was determined to return to Washington that day, which they did with fighter jets escorting Air Force One the entire way.
One weird note about the Doomsday planes and 9/11 is that one of those planes was actually seen above Washington, D.C. on the morning of September 11th and it added to the confusion and freaked a lot of people out. One of the Doomsday planes was also stationed at Andrews Air Force Base near Washington for Continuity of Government reasons, and on the morning of September 11th, as Garrett Graff writes in Raven Rock: The Story of the U.S. Government's Secret Plan to Save Itself -- While the Rest of Us Die (BOOK | KINDLE | AUDIO):
"Following standard crisis protocol, an NEACP [National Emergency Airborne Command Post -- the official name for the "Doomsday planes"] aircraft launched from Andrews at 9:43 a.m., using the call sign VENUS 77, and after considering flying to Offutt or to Ohio's Wright-Patterson Air Force Base, the pilots decided at 9:47 a.m. to just wait it out over Washington, eventually settling into a holding pattern over Richmond, Virginia. NEACP's unexpected presence in the skies, caught on camera by several news crews, added to the unfolding chaos around Washington. It's possible -- perhaps even likely, given a study of the morning's timeline -- that reports of the Doomsday plane over the capital are what triggered concerns to evacuate the White House and activate COG [Continuity of Government] procedures."
By the way, here's the picture that was mentioned in the question of the Doomsday plane in the background near Air Force One as President Bush arrived at Offutt Air Base on September 11, 2001:
