My headcanons for Dolores/Trumpet Girl:
She used to be a singer for clubs and lounges (pretty much wherever she could get work), but she either had too many uncomfortable run-ins with patrons and it drove her off or she suffered some kind of vocal trauma that made her really uncomfortable/self conscious about singing and she changed to playing trumpet at a less profitable establishment where she'd be more in the background. Either way I picture her having a deeper voice, and still able to sing, just embarrassed by doing it. Overall a pretty confident person otherwise, just really hung up on that.
I ship her with Dr. Teeth, and I think he'd help her regain some confidence in her singing, though she may still choose not to do it since she enjoys getting to have a more chill & low-key role in performances.
She's a total night owl and likes to go out on the town when she gets off of work. She's really good friends with Nigel even though they're total opposites (he's super dull and she's bursting with charisma and sass).
He used to moonlight as a bartender and they would try and help each other find work where they could, so sometimes she'll pretend she doesn't feel like going out and does a quiet hangout with him if he's been feeling really down. She's also one of the only people who finds Mahna Mahna relatively tolerable (if only in small doses).