According to the NYT piece I linked to above: "The suspect argued with some of the airmen before shooting one who was standing in the open door as well as the driver, Mr. Füllhardt said. The suspect was captured by a Hesse state police officer who was at the airport, which typically has heavy security especially following warnings in recent months that Germany would be a terror target."
and
"Mr. Füllhardt said that the dark blue-gray bus had regular German license plates, in line with American military policy to make vehicles less conspicuous, but that it still probably stood out from German vehicles. The busload of airmen had just arrived from England, he said, and had boarded the bus to go to the American military base at Ramstein, which lies few dozen miles to the southwest of the Frankfurt Airport."
According to longjack's article from Der Spiegel, the reports of an "argument" have "not been confirmed." So, piecing it all together, it looks like the shooter planned this (lots of extra ammo and told police he "pulled the trigger many times") and wanted to make sure the passengers on the bus were US military, then shot and killed the two easiest targets (the driver and the guy standing in the open doorway), wounded two more and ran into the terminal where he tried to mingle with other passengers but was caught by German security agents.
That sounds very likely. He was probably trying to make sure they were US military.
I wish the police or somebody had killed him rather than just catching him, though.