The principles are these.
1) The rooting media in the air layer needs to stay moist.
This can be accomplished in several ways. 1) sealing the rooting media tight to reduce mixture loss, or 2) adding water from time to time. Different ways of accomplishing the same goals.
Figs are easier to root than many other things, so what you can get away with when air-layering figs may not work with other things.
Quite often, with any air-layer, you need to add water to the rooting medium. Having the top open makes this easier, but also requires adding water more frequently.
2) Stripping off the bark below the air-layer is critical/necessary
when air-layering some plants, but not so much in figs.
The purpose of removing the bark is to interrupt the flow of energy from the leaves down to the roots, and redirect it to making new roots for the air-layer. Some plants, such as figs, root more readily than other things, and will generally still develop roots even if not stripped.
Many people will have seen a low hanging branch touch the soil and begin to root, without removing the bark. Same idea.
I developed the bottle method because I really didn't like the bag or plastic wrap technique - it was just kind of cumbersome and I wanted something simpler and easier (lazier?).
Use a smooth sided bottle as this will make removal from the bottle easier. And they are reusable.
Time varies with variety. I still find that Black Madeira takes longer to root, even when air-layering than most others. You can peel back the foil and check on it every so often, and then re-cover. No need to remove until the bottle is filled with roots.
The advantage over regular cuttings is that the root development is driven by the photosynthetic energy produced by the leaves, not stored energy in the cuttings.