A different take if you're interested:
In my homebrew setting, I have 5 types of magic. Arcane, Divine and Nature Magic are pulled from the magical weave (arcane using the 'background radiation', divine being sent by the Powers that Be, and Nature drawing from the Positive Energy Plane and Negative Energy Plane - the 'ends' of the weave). Psionic magic is internally generated and doesn't use the weave. Finally, Supernatural Magic comes from the world around us, but is not tied to the weave. It is true magic. Science, supernatural phenomena, etc... all use supernatural magic.
Bardic Inspiration, Jack of All Trades, Song of Rest, Expertise, and Countercharm are all SUPERNATURAL abilities in my setting. As anti-magic in my setting only impacts the arcane weave, you can use them when bound in an anti-magic aura.
Their arcane spell-casting and magical secrets are Arcane Magic reliant upon the Magical Weave, and thus follow all the tropes of Arcane magic.