I have made some changes as per your suggestions. Please have a look and suggest if it needs any more changes/additions.
Dear West Midlands Railway,
I am writing to offer my sincere apologies for not buying a correct ticket during my recent journeys. I am extremely sorry for any inconvenience or frustration that my actions may have caused, and I understand the importance of following the rules and regulations of the railway, and the importance of checking all the settings while booking a ticket online. Also, I now know to check my tickets carefully to ensure they are fully valid for use before I get on the train. I completely take responsibility for what has happened.
After the incident, I now understood my mistake and learned from it, and I am committed to ensuring that it does not happen again in the future. Now, I have switched to the West Midlands Railway app from the Trainline app to book my tickets after the advice from the Revenue Protection Officer to avoid any confusion in the future while booking the tickets online. I have now bought the 26-30 Railcard that applies to me to use for my travel. Also, I have changed the settings on my device to ensure that the correct Railcard discount is selected. I have understood how serious it is not to have paid the correct fare and how important it is to check all the options before proceeding to book a ticket online.
I would be grateful if you would allow me to pay the outstanding fares and your administrative costs in order to settle the matter without the need for court action and swiftly resolve this matter. Please let me know the amount owed and the payment process, and I will make the payment promptly.
Once again, I apologise for any inconvenience caused and I hope that we can resolve this matter as quickly and smoothly as possible. I am assuring you that I will always make sure that I travel with a proper valid ticket every time.
Thank you for your understanding.
It's fine to use AI to generate the structure of the letter but it still needs to be in your own words; this isn't, and it shows. AI-generated letters are full of pleonasms and redundancies. They also use American English, which is another tell. We say "apologise" with an s, not a z.
"Not being able to buy" is such passive language when describing fare evasion you should not use it. You make it sound like some other barrier was preventing you, yet your letter then says you completely take responsibility.
Take out some of the flowery language and don't use contractions like "I'll" (especially when you don't use them elsewhere); this is a formal letter responding to a criminal allegation.