expression
sorry to bother you when you're so busy
A set polite phrase used in business letters or emails to apologize for interrupting someone who is busy. Often appears at the beginning of a message.
ご多忙中、恐れ入りますが、ご確認のほどよろしくお願いいたします。
I'm sorry to bother you when you are so busy, but I would appreciate it if you could check this.
ご多忙中とは存じますが、ご返信いただけますと幸いです。
I know you are very busy, but I would be grateful if you could reply.
Combination of the honorific prefix ご, the noun 多忙 (busyness), and the suffix 中 (in the middle of). The phrase is a fixed polite expression used in formal writing.