That's mine. My bad.
是我的不好。

Yesterday was my bad.
That was my bad.
It was my bad.

Did I just spill water on your notebook? I'm sorry. My bad.
我是不是把水洒在你的笔记本上了？抱歉，是我不好。

Last night was my bad. I shouldn't have gotten so angry about what you said.
昨晚是我不好。我不应该对你说的话发那么大脾气

My fault
是我的错

My fault. I didn't see you there. Are you okay?
是我的错。我没看见你在那。你还好吧？

My mistake
是我的错

Yea I was the one who lost the report. It's my mistake.
是我把报告弄丢的。是我的错。

In the wrong
我的错

I was in the wrong about how to handle the problem. You were right.
对于如何处理那个问题是我处理错了。你是对的。