Another way to get a long story out is to use an argumentative listener.
The biggest problem with a long story is that, IRL, nobody sits and listens to a long story from somebody they consider an antagonist. Unless they are held at gunpoint, they will argue. If they can't argue, they aren't absorbing the story emotionally, they are thinking of retorts and derision. We don't have sympathy or empathy for somebody we think is a mean jerk trying to make excuses for being a mean jerk.
A second problem is that such stories often lack any sense of conflict for the reader: They tend to be written as an emotionless laundry list of facts, things that happened, things that were felt. They are full of "tell" with no "show", and when somebody is speaking it just doesn't sound natural for their speech to "show" what happened. They say "Then Jane got shot", they don't describe in metaphor and allegory what that looked like or felt like to them.
The scene as you describe it is not realistic.
We will sit and listen to a long story from somebody we like or love, we either want to hear such stories, or are willing to do them the service of providing a sympathetic ear out of friendship, even if we find it uncomfortable.
Having an argument (or at least questions from a child or student) in the scene can provide the conflict, break up the soliloquy, and make the scene both longer and more realistic. For example:
Nick is the Nerd, Bill is the Bully. At some point:
"You never gave a shit about anybody but yourself," Nick said.
Bill surrenders. "That's true. I'm ashamed of it, I wish I could have been stronger, or smarter, or a better human being, but I wasn't."
Nick is set back a step. "Yeah, right. Poor Bill."
"No, I don't deserve sympathy. I was a coward. I was too afraid to stand up to my father, and I tried to deal with my pain by inflicting it on others."
[Nick responds with derision; Bill is strong enough to take it without becoming angry, until the story is out. Nick moves from open anger to silent resentment until he finally changes the subject. Nic does not give in, but in the future the insults to Bill have stopped.]
In other words, I think the dynamic you have chosen is difficult to make work, it is rowing upstream to make Nick, the aggressor in your description, sit passively and hear Bill's story. In essence this makes Bill the bully again, he forces the nerd to sit and listen.
What would be easier is a role reversal, which you have already begun: the nerd is constantly picking on the bully, and the bully has withdrawn to the point of just passively taking it.
So continue that is what I am illustrating above (without knowing your characters, obviously). Nick is the angry aggressor, Bill has passively surrendered and provides information. When Bill cracks it isn't in anger, it is because Nick has won, his harangues have worn him down. In embarrassment and regret he would rather ignore this part of his life, but Nick won't let it go, so Bill gives up. It isn't anger, it is resignation, he has done wrong and cannot undo it, he knows that no matter how truly sorry he is apologies don't undo the harm and he has no right to expect forgiveness. The best he can do is let Nick know he [Bill] does not disagree.
Fortunately, you have cast Nick as a nerd, and nerds can think. IRL, sometimes understanding how something bad happens can help us deal with the fact that it happened to us. So let us say Nick realizes that Bill is a different person, and now HE [Nick] has become almost exactly the same kind of bully he despises. The nerd can figure that out, and feel shame at having let himself get so far out of control, and that can let Nick relate to how Bill himself felt back then. So Nick turns over a new leaf, too. His retaliation against Bill is done, he does not want to be a bully. He now understands first hand the grim reward of insults and inflicting pain on somebody that won't defend himself, but that is not who Nick wants to be. Which means now, his relationship with Bill is reset to neutral, and once he has been mentally diligent enough to kill this ugly pattern of behavior in which he responds to Bill with attack, their relationship can move forward.