Simpson said he initially resisted the smugglers' suggestion on the grounds that cross-dressing smacked too much of a pantomime.
"But when we put on the burqas, I realised how sensible it was. We seemed to disappear from view.
"For the entire length of the journey, no one looked at us. We hunched in the back of a pick-up truck, keeping our hands and walking boots covered up."
Simpson said the burqa was comfortable in some ways, but it sat tightly round the forehead.
Both men soon began to show "large, unfeminine sweat patches" above their lace panels.
Simpson, who has worked for the BBC for more than 30 years, has reported from more than 100 countries, including 30 war zones.
From Nangarhar he said thousands of Afghans were fleeing towns and cities and joining their relatives in the countryside out of fear of an American attack.
The Taleban, which originally had some support for restoring order, had become as unpopular as previous Governments through its corruption and mismanagement.
"Now, neither the Taleban nor anyone else thinks they can conceivably survive for long in the face of an all-out American attack.
"Reports from several parts of Afghanistan speak of Taleban commanders slipping away and joining the exodus to the countryside."
Map: Opposing forces in the war against terror
Afghanistan facts and links
Full coverage: Terror in America
