The mayor also takes along a police detail when he travels, flying two officers on his private plane and paying as much as $400 a night to put them up at a hotel near his house; the city pays their wages while they are there, as it does whether Mr. Bloomberg is New York or not. Guns are largely forbidden in Bermuda — even most police officers do not use them — but the mayor’s guards have special permission to carry weapons. A spokesman for the Police Department declined to comment.