
Characters who are withdrawn, reserved, or otherwise disinclined to participate in social activities generally require external factors to spur them on. Either there needs to be some kind of external conflict or events that force their participation or there needs to be other characters present who are willing to sort of wheelbarrow them around to a comfortable place for interactions.
I've roleplayed plenty of characters who are asocial or anti-social, but generally I only do such when I am engaged in a plot; by their nature, these kinds of characters generally don't care to be involved in things unless they are forced to, or unless they are directly affected. Otherwise, they don't really work in slice-of-life situations except as background.
So I'd look to getting involved in a plot or engineering one yourself first and foremost, to get the best possible use of such a character.
I've roleplayed plenty of characters who are asocial or anti-social, but generally I only do such when I am engaged in a plot; by their nature, these kinds of characters generally don't care to be involved in things unless they are forced to, or unless they are directly affected. Otherwise, they don't really work in slice-of-life situations except as background.
So I'd look to getting involved in a plot or engineering one yourself first and foremost, to get the best possible use of such a character.