Example sentences
duì对bù不qǐ起，wǒ我chí迟dào到le了。
Sorry I'm late.
shuō说shēng声duì对bù不qǐ起ba吧。
Just say sorry.
About this word
对 is "to face" and 起 is "to rise, to come up to", so the phrase is "cannot face up to you". The grammar underneath is a potential complement: 对得起 means "to be worthy of someone", and swapping 得 for 不 flips it to the negative, failing to measure up. That same 得/不 slot explains 看得见 and 看不见 (can or cannot see), 买得起 and 买不起 (can or cannot afford), 睡不着 (cannot fall asleep). So 对不起 is an apology shaped like a small admission of failure.
The story behind the character
对
对 started life as 對. The right half is 寸, a hand. Xu Shen split it into 丵, 口 and 寸 and glossed it 對, 譍無方也: answering, whatever comes at you. From answering it slid into facing something, then into being right about it. 对不起 is a reply that does not measure up to the other person.
不
不 is the basic negator: put it in front of a verb or adjective and you have said no. 我不喝 I don't drink, 他不高 he isn't tall, 不客气 you're welcome. It covers the present, the future, and plain refusal. For the past, and for 有, Chinese switches to 没 (我没有钱). One sound rule: before a fourth tone, 不 is pronounced bú, as in 不是 bú shì.
起
起 is 走, a person moving, with 己 for the sound. Xu Shen wrote 起, 能立也: the ability to stand up, before any walking happens. From standing up it spread to starting, rising, getting out of bed. 起床 is rise from bed, and 一起 uses the same character for doing something alongside someone.