Bush - described in dry police style as a "falling/moving object" - was treated for scratches on his hands and arms after he went tumbling during a break from the summit in Gleneagles, Scotland, last July.
Although the accident was reported at the time, the police incident report, published in Scotland in a Sunday newspaper, gives further insight into the chain of events.
The unidentified officer had been with a detachment of constables, dressed in anti-riot gear, guarding a road junction when the president cycled up.
"(At) about 1800 hours the president approached the junction at speed on the bicycle. The road was damp at the time," the police report said.
"As the president passed the junction at speed he raised his left arm from the handlebars to wave to the police officers present while shouting 'Thanks, you guys, for coming'.
"As he did this he lost control of the cycle, falling to the ground, causing both himself and his bicycle to strike (the officer) on the lower legs."
"hit by moving/falling object"
Official British police report of encounter with a tumbling US president
The officer fell and hit his head on the ground, the report added.
Meanwhile "the president continued along the ground for approximately five metres, causing himself a number of abrasions," it continued.
"The officers... then assisted both injured parties."
Bush later telephoned the hurt policeman - who damaged his ankle ligaments - to ask how he was and to apologise.
The injury was officially recorded as being "hit by moving/falling object".
The newspaper suggested that in Scotland such an accident could have meant police action.
Earlier this year Strathclyde Police issued three fines to cyclists as part of a crackdown on careless riders.