I know you are busy and I shouldn’t bother you again.But for

I might bother you for you are busy. But I have to write this letter due to its urgency, and hope you would not mind it.
觉得你这个句子重复意思有点多.

觉得这样会好一点
I know you are busy and I shouldn’t write this letter to bother you again. But the time is limited.I hope you won’t mind.

可以这么说,没什么不对的地方,都可以看懂我的建议
I know you too busy to mind me, but I real have no choice, time is limited, Ihope you can help me ,I worte this letter hope you won't be bothered
Yours!
我知道你现在很忙而没...

I know you are busy and I shouldn’t bother you again. But for the time is limited, I write this letter. I hope you won’t mind.
很好，也可参考如下说法：
I know you are busy and I really don't want to bother you again. But because the time is urgent, I have to write to you. Don't mind for that. Thank you.