"don't mention it" and other expressions (esp. for Chinese)

I was recently watching a Chinese learning DVD and one of the expressions they were teaching was:

"duibuqi" which means "I'm sorry"

Their example was when you accidentally bump into another person, you would say "duibuqi".

If someone says "duibuqi" to you, you say "mei guanxi" in return.

The DVD translated "mei guanxi" as "it doesn't matter" or "don't mention it".

I thought about it and realized that that was not the best translation.

In English, if you bump into someone by accident you can say any of following:

       sorry
       I'm sorry
       I'm so sorry (if you really bumped them hard, or caused a problem liked spilled your coffee on them!)

The person who gets bumped into, and is told "I'm sorry", can respond with any of the following:

      it's ok
      no problem
      no worries *this is an expression that has become more popular recently. When I grew up, people just said "no problem" and never "no worries", but now especially younger people say "no worries".

"It doesn't matter" isn't wrong, but I would probably say "it's ok" instead.

Saying "don't mention it" if someone bumps into you and says "sorry" seems incorrect to me.

Here are some examples of when of when you might use "don't mention it":

        You are going to a café with a friend and you forgot your wallet, so your friend buys something for you. You say "thanks!" and your friend says "don't mention it", like a form of "you're welcome".

or

        You ask a friend of a friend for a ride home and they say they can give you a ride. You say "thanks a lot!" and they reply: "don't mention it". It's literally like "don't mention" the thanks, because it's nothing, it's not an inconvenience.

So, "don't mention it" is used when someone, perhaps even a stranger, does a kindness for you, in response to your saying "thanks", not in response to your saying "I'm sorry".

In fact, "don't mention it" might not be that commonly used.
More often, you will hear: "thanks" and (in response) "you're welcome".

Of course, the combination of "thanks" and "don't mention it" is a special one, only used when you are saying thanks because someone has done a kindness for you which may be a slight inconvenience to them. That also might be true for "thanks" and "you're welcome", but it's not the main meaning of it.