大変お待たせしました（レストランで）って英語でなんて言うの？

This is a common way in American English to express in the context of a service that you want to apologize about the amount of time that the client had to wait. I hope that this helps. :)

By saying 'I'm sorry' or 'sorry' then you are telling someone politely that you are sorry something has happened. you could simply say 'to keep you waiting' or if it has been a long time could say 'for keeping you waiting so long' Thanks for your patience is saying that you are thankful to the customer for waiting for a table you could add 'I apologise for the wait meaning you are sorry they have had to wait

Saying that you are sorry to have kept the customer waiting is a polite way of acknowledging that they have had to wait a long time and that you apologize for it. Thanking the customer for waiting and being patient is another very polite way to show that you appreciate their business and that

The two sentences you see provided above are terrific ways to express to your listener that you are sorry they had to wait for a long time. In the second sentence you will see the word bit. Although this word has different meanings in this sentence it means a large amount. This word is commonly used in our everyday conversation.

Well, if you learn one word from all the suggested phrases above it should be the word 'queue'. Use this word instead of the phrase 'line of customers' or 'line of people' in any situation. In the UK we never say 'line of people, yet so many students mistakenly believe this is good English.