So when you say
"You add 3 dice to your current Luck total, so if my Luck is currently at 7 (from the above example) I would throw 7 dice from my Luck and 3 from the bow. Note you cannot "lose" failed dice from equipment, so it may help to use different color dice. The breakage check is done after using the item (not as a part of the same action, that could be punishing) with a single d6."
That it means that all rolls count for the encounter and then if any dice (7 for the Luck and 3 for the bow) are a six the bow is broken after.