Like you passively have I dunno 3 AP a day, which is used to use abilities. It does not accumulate. Some abilities would cost 0, 1, 2, or 3 AP.
In fact you could mash-up the ideas. Get a winning streak and you start getting bonus AP banked that DOESN'T expire at the end of each week, that you can use at any time. Collect a bounty you get bonus AP banked in a similar way. So if you want to hellmurder someone with abilities you can do so by winning many times in a row or by kingslaying.