Prosecution letter from tfl

Hi everyone, I’m looking for some advice regarding an issue with my cousin’s 11-15 Oyster card. I was recently on a bus and used her card, explaining to the officer that I was planning to return it to her, which I genuinely intended to do. I mentioned that this was my first offence in my letter back in hopes that they might be lenient and settle the matter without a penalty.
However, I’m a bit concerned because I think I might have a prior offence from about 4 years ago. At the time, I didn’t tap my card at a station because I was in a rush. I’m not sure if that penalty ended up in my mum’s name or mine, as she was the one speaking to the officer then.
Has anyone had experience with a situation like this? Do you think TfL might still consider this my first offence despite the potential prior issue and will settle or Any advice on how to handle it would be really helpful.
More info is
Im 20 with no job apart from gambling income which is quite a bit and using my child trust fund as a mean to live
This is my first bus offence apart from that train incident 4 years ago still dont know if its in my mums name or not
In the letter I’ve already admitted fault, apologised sincerely, and sent a written request to settle the matter outside of court — including offering to pay any reasonable amount.
Just need some advice
Also im asking if they do settle as ive had a friend of mine whos sister was caught using somebodys card for years and when she got a lawyer tfl settled for £500