Best Answer - Chosen by the AskerIn reality, when we say that 'I am sorry' in Chinese, generally we won't say 'I am' as it is in English, especially in spoken Chinese. Notice: I said 'generally', most of the time, not 'abosolutely'. This is not about grammar, it's just how we use language in daily life. So you could say:
实在是对不起。 honestly, sincerely
真的是对不起。 really
真的是不好意思。
真的是非常抱歉。
Among them,"抱歉"is the most polite and cultivated expression.
e.g.我迟到了,真的是不好意思!
As for some formal situations like presentations, writings etc, we would say: I feel very sorry about...对于....我感到十分歉意/抱歉.