Scott Johnson's Welshmen romped to a resounding 27-3 victory over last year's RaboDirect Pro12 runners-up and Heineken Cup champions Leinster in the season opener.
Bradley admits his own side need drastic improvements from their 38-15 defeat against Cardiff Blues at Murrayfield to match the sparkling Welsh outfit's form from last week.
But if Ospreys feel that taking all the points from their clash with the Gunners will need any less effort, Bradley has vowed to make them pay the price.
"They beat a strong Leinster side so they'll be very confident coming off that victory," said Bradley.
"In a way, that's good for us. We have a point to prove and they might be a little bit overconfident.
"The challenge that we face, they are a young side sprinkled with some very experienced internationals that have been left at home.
"They are a side that like to play the ball and keep the pace of the game up with quick tap-ins etc. You'll see them do that, we are aware of that, we need to counter that.
"But that suits us as well in terms of the pace of the game, we will go toe-to-toe with any side that wants to play that type of game so hopefully it will make for a good exciting game and potentially a win away from home for us."
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