However Edinburgh, inspired by 17 points from RaboDirect PRO12 man-of-the-match Leonard, ultimately made light work of the trip to the continent.
A score from Ross Rennie completed their points haul but while Leonard's kicks at goal stole the headlines it was his open-play prowess that pleased Bradley.
"Harry played well and backed up his performance against Leinster," said Bradley.
"It's important at No. 10 that you control the game and he did that. It was a good performance from him, he took his kicks and struck the ball well but his most telling contribution was his ability to pin Treviso back into the corners and keep the pressure on them."
And Bradley admitted it was a nice feeling to bag their first win on their travels this term.
"It was a good and important win for us," he added.
"The boys played well in terms of our shape, our control of the game from start to finish, and also that we put away the bogey of not winning away from home this season.
"We managed to direct our play into situations where we weren't in a lot of pressure, we didn't over play the game, we scrummaged well and we nullified their maul, which were all key elements in allowing us to win this game."
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