They cannot arrest you/take you into custody on behalf of County B unless there is a court order directing them to do so. That court order takes the form of an arrest warrant. If you have taken care of business on the new case in County B, and there is no warrant out for your arrest, police department in County A can't do anything to you.
If there is a warrant out for you from County B, it is either a no-bail warrant or a warrant to which a bail amount is attached. If it is a no-bail warrant, County A will apprehend you and hold you in custody until you're picked up by County B. On the other hand, if there is a bail, you can post the bail and be released in County B. Sometimes, in large counties where they don't want to bother with a non-violent misdemeanant from another county, they will just cite you out on a low-bail arrest/bench warrant.