Reading articles about Barnes, he is described as a "tearaway" early in his career who later became a fast-medium bowler before perfecting his leg-breaks.
"What sort of a bowler was Barnes at this stage? Gone was the “tearaway” aspect of his early career and in its place was a fast-medium bowler. Barnes was tall and slim with a smooth run up that began slowly before he accelerated and lengthened his stride finally leaping into his delivery. Much of his pace came from the long swing of an exceptionally high arm. He had not at this stage quite perfected the leg break that was to cement his reputation but it was in development and he was able to swing the ball as well as bowl an off-break at pace."
What is remarkable is that, due to injury and clashes with officialdom, he played only 27 of a possible 58 tests during his Test career. Of these, just 10 were played at home on bowler friendly English wickets. He played 13 Tests in Australia and 4 in South Africa and his figures were in no way flattered by regularly cleaning up tail-enders. He claimed Victor Trumper 13 times and Clem Hill 11 times - not bad victims!
On the 1901/02 Ashes tour of Australia, "after seeing how hard the pitches were Barnes decided that speed, while retaining control, should be his priority, and while he was not to be genuinely fast, he certainly had sufficient pace to be able to bump the ball disconcertingly at the Australian batsmen when he chose to do so."
It is generally regarded that Barnes developed his leg spin around 1903 - 1905 and he used this as a variation to his faster deliveries while maintaining the same action.
Ten years later, at the age of 39, Barnes was still opening the bowling for England in an Ashes series. His pace had understandably diminished yet he "used the new ball wisely and his match hauls were remarkably consistent, 8 wickets in each of the second and third Tests, and 7 in each of the last two."
The idea that Barnes just bowled medium pace spin stemmed from observations of his bowling late in his career. This would no doubt have been reinforced when Bradman mentioned both Barnes and O"Reilly in the same breath.