Used in casual conversation, not in formal situations like business meetings or official documents. When we meet for coffee, I have a bone to pick with you about the party last week.
Pro Tip 2/3
Personal Dispute
Usually refers to a private matter or minor personal issue, not a large public or professional conflict. She's got a bone to pick with her roommate about cleaning the apartment.
Pro Tip 3/3
Need for Resolution
Implies the speaker wants to discuss the issue soon and clear the air, rather than ignore it. He said he's got a bone to pick with me about the project—I think he wants to sort it out today.