You went by your coworker's office to talk with him about a problem you're having, but he said he was too busy to talk to you. You're a little annoyed, but you want to respond politely because you're at work. You say:
OK, Sorry to bother you.
To "bother" someone means to annoy them or take up their time. So the phrase "Sorry to bother you" is an apology for using up some of a person's time.
Here are some situations in which you can say "Sorry to bother you":
When you ask someone a question that they don't know the answer to, you can respond with "OK. Sorry to bother you."
A: Do you know where the nearest subway station is?
B: Sorry, I'm not from around here.
A: OK. Sorry to bother you.
You can also introduce a question with this phrase. Especially when you're talking with someone who's important and busy in a business situation, you can start your question like this:
Sorry to bother you. Can I ask you a quick question about the budget report you sent me?
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