I guess I'll wait until everybody makes it to the inn first before I post, I guess. I just have to figure out her approach. The only way I could see this character approaching the party is if she assumes they're adventurers, and she's looking for a party.
As for backstory, I actually didn't have a lot thought up in advance. Though one idea I have to go off of is a sort of nod to Samurai Champloo, where she introduces herself as a caster looking for a wizard who smells like daisies.
Also, I feel like making it so she learns to gain more control over her magic, which I've decided is made so "random" through her Band of Chaos, a trinket that unlocks an unfathomable array of spells no spellcaster could possibly remember all at once, all managed by being chosen at random. I think an improvement she will make down the line is sort of an attempt to put the spells into "categories" in order to get better use out of the spells she needs while still having some RNG to deal with.