今日はアルバイトがあるから無理だって英語でなんて言うの？

This is a nice phrase to use with friends, it gently lets them down but at the same time you are expressing that you would have loved to have hung out with them. "I wish I didn't have to work". If you want to make it more polite. You can add an apology on - "I'd love to hang out but I have to work, sorry!" "I'll catch you next time!"

"I would love to come but unfortunately I have to work." This explains to the person that you are not available because you have to work. "I'm sorry I have to work so won't be able to come." This politely explains to your friend that you would really like to see them but you cant because you have to work.

When something or someone is more important than something or someone else, you may describe one person or thing as 'taking precedence' over another.' "At the meeting, the subject of membership fees took precedence over everything else." If you say you are 'otherwise engaged' it means that you are doing something at that time - and usually, that you do not wish to give details of what you are doing (or the details are not important). If you say, "I can't make it," it means you cannot attend.

I would like to, but I have to go to work.' explains that although you would enjoy spending time with your friend, you need to go to work. 'Unfortunately' is another way of saying 'sadly' or 'unhappily' 'I have another commitment' mean you are already 'committed' or tied to doing something else, in this case, your part-time job.

"I wish I could, but unfortunately I've got work." shows that you would like to do something but regrettably have work.

All these would be a good way to explain you have to work instead of hanging out A part time job is a job you only do for a few hours a day/week So to say "im sorry i have to go to work instead" would be a simple way to say it