A year ago I made a really awkward mistake with a couple of women. I would've brushed off like normal people would do, but they've been very persistent with trying to talk to me, but I just can't idk why. I get so scared because I don't want to make things awkward again, or I'm afraid I'll escalate things in a really bad way and since the only time I see them is in a public setting. I don't want to make a scene.

Is there a correct way to apologize to girls because I know I made a mistake, and they know too. So is it worth apologizing? Ik saying "I'm sorry for x" but I feel like that won't cut it.