@Steve Ford thinking in line with my thoughts - I think there is stiction of the seals on the pistons in the calipers - the seals are pulling the pistons back again, leaving a large gap between the pads and the rotor, hence the double pump to get it to close and work. Then they get retracted again by the elastic nature of the seals, after the pressure is off. Normally they should be 'self-adjusting' effectively only retracting so pad is only marginally off the rotor (almost touching but not applying any braking force).
You recognize this effect when you install new pads - you push back the pistons to create the space required for the new thicker pads; then, even with bleeding, when you pull the lever initially it will not yield any resistance and you need to 'pump' the lever several times and then it will be rock hard all of a sudden - this is because there is not resistance as the pistons/pads are moving only very small distance and require multiple pumps until that gap is closed up; of course then it should stay there. So the double pump is kinda doing the same thing, it needs to move the pad initially and then again with the second pump. You are talking very small distance here, compared to the lever travel.
You might actually find new pads would at least temporarily 'fix' it, as the pistons would have to be pressed back into a different position within the caliper cylinder than the current pad thickness allows. But it will likely return again.
If still under warranty I would request new set of calipers and of course yet another bleed would be necessary. I hate to disagree with Steve since we are essentially on the same page, but whether you or the shop does the work, the calipers need to be stripped and cleaned and new seals (& maybe even pistons replaced). But under warranty I'd be insisting on replacement calipers.
Incidentally Speed Triples underwent a very similar problem with the 05-06 S3's with Nissin calipers - Triumph did not do a full recall but offered a 'goodwill' replacement of the pistons with those from the Daytona 675, for anyone who asked.