You can put each action on as many bars as you want.

The game does an especially bad job of teaching BLM compared to the other jobs, due mostly to a lack of documentation or in-game indication of the exact effects of Umbral Ice and Astral Fire. Every other job explains their potency adjustments in tooltips--for example, as combo potencies or positional potencies--but BLM's spells don't do that so new people don't have any recourse but to ask.

In general, you don't have to worry about another case like Fire III. You can use new spells as you get them. It may not always be optimal to start using them immediately, but the difference between an optimized rotation for the current level and a rotation that includes a new spell is less important than getting used to using the new spell correctly, so don't worry too much about it.