Option: Temporary AP (Last Second Saves)
Most games hand out AP at the end of the session, or at least don't allow it to be used until either the end of the night's gaming, or until a chapter break where the characters have down time to train. This is the general model I've envisioned for D&B. However, at the expense of a little extra bookkeeping, AP can take on a new use, and become another critical resource.
Under this concept, AP is given out on the fly, and is tracked with tokens or a different part of the sheet. These points may be spent at any time, for things like:
- Healing a point of damage
- Adding a die to a roll
- Negating the -1 penalty modifier
- Improving odds of a scarcity Roll
Option: Group AP Pool (Settlement Advancement)
Long term games, especially those in the Anarchy Zone setting, involve trying to (re)establish some form of society or secure area. Of course, much of this depends on what the players are able to find through innovation, and who they recruit through role-play. But it may be ideal to introduce a point buy system for upgrading a homestead, giving players a choice between working on personal improvement, healing, or granting their time and labor to communal projects.
In this variation, at the end of a session, the players may spend AP as normal, or place them in a group pool. This mutual bank can in turn be used to acquire upgrades to facilities, vehicles, or equipment used by everyone. "Town Stats Part One" gives an overview of what might be involved - Required attributes like population start cheap, but go up exponentially (recruiting a half dozen people easy, a few hundred - less so). Helpful ones have a more linear progression in cost, but are caped by the required attributes. (You can't have more soldiers than total population after-all.) Advanced settlement attributes would be quite expensive, but could pay some sort of dividend over time.
So how often are AP to be handed out, and for what? It depends on if any of the above options are used, and how long the campaign should last. One constant, however, is that points should be handed out for actions of the players, not the characters. AP are a reward for quick thinking or good acting, not luck in rolling.
As stated in the rules, a new skill costs three points, and advancing a skill costs twice the next level (ie two to three is six, three to four is eight). Three or four points a session is going to be rather slow advancement, especially if there is a focus on healing over advancement, but scarcity is the name of the game. Giving about six points a session gives a bit more breathing room. If either or both of the rules above are used, eight or ten points might be advisable to keep players leveling up with some regularity. Conversely, five to six points can keep them struggling for a while.
Generally, it is the game master that hands out AP, but they should be open to suggestions from the players. If the others appreciate the plan, or respect the depth of role-playing, then they can certainly recommend their comrade for recognition.