Simple ... you must use your shrouds prior to your attack, and a miss deals damage equal to a shroud less. The mathematicians have already calculated that every other round is the best for DPR. So simply shroud-and-attack every round, you may not get your bonus damage, if you miss.
I quite like what I've seen of the Assassin so far.
Every other round is NOT best for DPR. Waiting as long as possible is best for DPR.
Think of it this way. You have your hit damage, and your miss damage. Your hit damage is a straight y=mx type equation. If you hit you get no bonus for waiting, you do precisely the same damage per round no matter when you attack.
But your miss damage is different. The equation for miss damage DPR, if X is number of shrouds and D is damage, is (X-1)D/X. That's shroud damage for all shrouds but one, divided by the number of rounds it took you to get to that point.
If you like, go ahead and graph Y=(X-1)D/X. You'll see that as X grows, the equation approaches a limit of Y=D. Y is DPR from misses in this case, and every round you wait increases it. Of course you get diminishing returns the longer you wait, but there's never a point where waiting isn't strictly better than not waiting.
This is of course in a mathematical abstraction that doesn't deal with issues like your shroud target getting killed by one of your allies while you're busy building up more and more shrouds, or the uselessness of having 50 shrouds on an enemy with 5 hit points, and of course you can never pass X=4 in the actual game.
But in mathematical abstraction, every other round is NOT the best option. Waiting for the full four rounds is best.