In our son's case, it was just a matter of time, and growing self confidence which happened in the work place via nurturing colleagues. We saw him in person every month or so once he'd left home and moved to his job, and could see how he "grew" into being more confident, just by being around other adults 7 hours per day in a professional/respectful workplace.
It certainly didn't come by some random people bullying him by telling him he was too quiet!
His workplace is very open to ND people (not that son is diagnosed with anything), but ND awareness helps people who are just naturally a bit quieter/shy without a label. It's the nature of his profession really, and attracts a lot of "geeks" who are Maths geniuses. One example is them having "quiet" rooms where they can go to chill out if things are getting too much for them - no questions asked, no challenges however busy, and guaranteed no disturbances. DS has only used it once, but he said it was a massive comfort to know they were there if things got too much, so it enabled him to push his own boundaries, knowing there was a safe place if he ever needed it. Just go in, put the "do not disturb" sign on the door, and you're left in peace, and can come out when you're ready and no one bats an eyelid! That's the kind of thing to really boost self confidence - the ability to try something and take a risk - no comebacks, no questions asked, if things go wrong!
Schools have it massively wrong with the bullying of "out of the ordinary" pupils by teachers, whether it's the classroom, the sports fields, the gym, etc. Whether it's not being gobby in class, or poor co ordination in games lessons, etc. "Team work" isn't nurtured, you basically have to get on with it and are bullied by the teachers if you don't. That's the opposite of the gentle persuasion and confidence building that they should be doing and does cause more harm than good. No one is going to be a better sports person or less shy/quiet by someone telling them to be better or talk more.
They need to be encouraged, not criticised.