申し訳ないけど間に合わないから行けなくなってしまった。って英語でなんて言うの？

It is polite to start the bad new with an apology, it makes you seem more sincere. If you want to be vague you can use 'something came up' it politely informs the person that you have to attend to something else it also does not need a follow up excuse. 'Bail' is informal language, we use this when we want to cancel on a plan.

If you have 'commitments' it means that there are 'pressing' matters that you have to attend to - this may be in the form of being responsible for another person, or having to be on duty at a work location. If something 'comes up' it means that something arises during work or even in your free time, which requires your immediate attention

By saying you will make it up to your friend, you are showing that you are sorry in another way other than just saying sorry.

"I'm sorry something came up at work so I won't be able to meet up." This politely apologises to your friend and explains to them that you will not be able to see them that day because you have to stay at work. "Sorry but I am court up at work, I will have to rearrange." This apologises to your friend and asks them if you can make plans to meet another day because you are still busy at work.

If you are not able to make a meeting then you would say 'I'm so sorry' or 'I'm sorry' this means that you are sorry for not being able to make it It is always nice to explain why you can't make it as well to be polite so you can say 'I have to work' and add 'I won't make it today' to explain that you won't be coming

If you were suppose to meet your friend for something of leisure, then you can say, "I'm sorry, but I can't make it this time. Can I take a rain check?" The phrase 'rain check' is used when you had plans to do something but need to postpone them for a later (but unknown) date. So here, you are asking the person if you can reschedule the meetup. For formal and casual situations, you can say, "Sorry, but can we reschedule? I have to work today." This is a polite way to ask if you can meet another day.

To show your regret, start with your apology; “I am so sorry.” Then explain clearly why you will have to cancel your plans; “I have to work.”