For a quiet instrument, find places with resonance. Start in subways, also porches if publicly accessible.
For repertoire, start with accessible tunes, even if they're not specialist repertoire. You add that in later to break the pattern of predictability.
I once had a someone who turned up in clarsach class, really after a taster. The teacher was out of the room, there was a spare harp, I sat her down behind it and showed her basic hand position. By the end of the class, she'd rented a harp and then hit a problem, practicing wasn't too feasible in her house for some reason, so she took it outside onto the street. Worked on her first tune, Greensleeves, and in half an hour she'd more cash in front of her than she'd earned that day as a temp. The book we were using was Sylvia Woods's harp primer, which isn't inaccessible to dulcimers either - things like Robin Adair, Greensleeves, Si beg si mhor, some of the O'Carolan planxties. Also include more recent repertoire, Paul Simon, Leonard Cohen's Halleluyah, Dylan, show tunes, current hits. But do one at a time until it's right. The same happened every day, so by the end of the week she'd stopped temping and was a full-time busker, learning repertoire as she went. By the end of the month she knew more tunes than anyone else, and within a year had turned pro
Another tip is to seed the pot. Just four or five small coins, not too much, but enough to suggest other people liked it. Also keep it drained, a full pot suggests you don't need more. Of course, being female did no harm.
I keep coming back to this to add more: another thought is soundbites. If someone stops to listen, a mini performance, something to hook them in, something for show, then a slower piece focusing on melody, and then a blow-off, really showy. Maybe don't be afraid to ask for cash, even!
Another part of what you said suggests you need to work on your own resonance - not daring to sing. Solid singing practice means you cannot help but sing in resonance to the city around you, and that then chooses what you play. It may be you want to sing in a nasal tone - don't, find your diaphragm "inspiration point" and sing from there. The way to do that is to relax down and find the point at which your inhalation turns to exhalation - sing from there. Project the sound outside the skull and it'll be nigh on impossible to sing nasally, but more to the point you'll have a starting point for volume.
That resonance question is very much of the order of the day when it comes to hearing where to play. Too much background noise and you get drowned out, but you need footfall as well. Also be aware there are protocols amongst buskers which differ from town to town. Some prioritize pitch, others first come first served, and there can be constraints from local authorities: TFL, for instance, asks for a fairly simple proficiency test and then you play on set pitches, often with good acoustics, but limited for an hour.