Duibuqi, buhaoyise, paisei

bao4qian4 抱歉 = shihle 失禮 It’s rather formal. Use it in business or service occasions to apologize to your customers for your fault. 「我為此感到相當抱歉。」I’m so sorry for it. (Politicians sometimes say it.) 「很抱歉，您的帳戶已經不存在了」。 We’re very sorry. Your account is no longer valid. 「抱歉，讓你久等了」Sorry that I kept you waiting.

buhaoyishi 不好意思 = painnse 歹勢

1. Excuse me. 「不好意思，借過一下。」 Excuse me, please allow me to pass
2. to be apologetic and embarrassed a) 「不好意思，麻煩你了。」I’m rather embarrassed (by my inability), but please do it for me. I’m counting on you. b) 「讓你擔心了，不好意思。」I’m sorry that I made you worry about me.
3. “You shouldn’t have to”. 「你太客氣了，真是不好意思。」You’re being too courteous. You shouldn’t have to.
4. to be slightly apologetic a)「 不好意思，賣光了。」 Sorry, it’s sold out. b)「啊! 不好意思、不好意思。」Oops! Excuse me (that I bumped against you, but it’s not a big deal.)
5. to be perfunctorily apologetic「不好意思，你打錯了。」 Sorry, you had the wrong number.
6. to be shy and/or embarrassed 「我不好意思問他。」I’m too embarrassed to ask him/I’m too shy to ask him.

dwaybuchee 對不起 Less formal than 抱歉, especially in written form, but not necessarily weaker. It has no connotations of feeling embarrassed. You know you’re wrong, so you apologize. Sometimes, you can still use 對不起 even when you’re only perfunctorily apologetic or slightly apologetic, if you feel the urge to show more respect to the other person. You can also add qualifiers to buhaoyishi to make it almost the same as dwaybuchee. For example, 真不好意思，非常不好意思 is essentially the same as 對不起。

You say 對不起 to your boss or your girlfriend. You always want to appear remorseful. You don’t say 抱歉, because your boss or girlfriend is not your customer. Now if you’re very remorseful, truly remorseful, you add qualifiers like this: 真對不起、非常對不起。

In Taiwanese, you don’t say 對不起duibuhki. You say失禮/shihle sorry; 真失禮/jinnshihle very sorry; 真正足失禮/jinnjiannjokshile truly, very sorry; 非常失禮/huishongshihle extremely sorry. Notice 失禮 is already formal. You’re sorry and you mean it and can never be too formal.

*In bother Taiwanese and Mandarin, you say 「我對不起你。」I let you down. Notice 對不起 here is a transitive verb.