The result gets Edinburgh's Heineken Cup campaign back on track, leaving them level on points at the top of Pool Two with the Blues with two matches remaining.
And Bradley revealed he was not surprised after the effort his charges had put in the week before in training.
"We did so well in the breakdown and the contest from a physical point of view. The rest of our game fell into place for large portions of the match," said Bradley.
"I think it was a much-improved performance by us on last week. Cardiff did very well last week at the breakdown and they physically dominated us.
"The boys were very, very good this week. The consistency of performance was better in terms of the quality of the work at the breakdown.
"More players got it right and it made a huge difference to us - we were able to put a lot of pressure on Cardiff, particularly in the first half.
"After four matches we're joint top of the group. Hopefully [the losing bonus point] won't be a key factor at the end of the pool.
"As a performance that was a very good performance. We've three wins out of four in this competition. It's not a bad start."
Meanwhile the Ospreys' Heineken Cup hopes took a major hit as they slumped to a 16-13 home defeat to Saracens, a first European defeat at the Liberty Stadium since 2005.
Ernst Joubert scored a first-half try for the visitors before Ian Gough's second-half effort gave Scott Johnson's side hope.
However Saracens held on for the win to leave themselves in prime position to top the pool and secure a spot in the quarter-finals.
In the other game in the group 14-man Treviso were unable to repeat their heroics of last week as they went down 29-12 in atrocious conditions in Biarritz.
Franco Smith's side were dealt a huge blow when back row Francesco Minto was sent off for a headbutt midway through the first half.
And despite leading 12-3 at the break, the Basques were able to turn it around with the wind at their backs, hooker Arnaud Heguy grabbing the crucial fourth try to keep Biarritz's quarter-final hopes alive.
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