Bells on fire apparatus were a holdover from the days of steam power. All steam engines (ships, locomotives) had bells as warning devices and so too they were included on steam fire engines. They complemented the steam whistle of the pumpers, which only worked when the boiler was fired while responding. Gongs were placed on ladder trucks, mounted on the front floorboard and operated by the chauffeur via a foot peddle.
In the days before radio communications (prior to the early 1950's) units were out of touch once they left quarters. They were required to return immediately and as fast as possible in order to "tap back" into service. The bells were used to clear traffic to get them home quickly. (No stopping at the supermarket for the evening meal or other nefarious events in those days.)
Sirens were introduced with motorized apparatus but the bells were used with them to respond and upon returning to quarters. Anyone old enough can remember
the bells clanging as a company approached an intersection. The floorboard gongs on the trucks were eventually replaced by a regular bells, usually mounted between the ladders of the trailer and rung by a man riding the sideboard. Since tractors were replaced more frequently it was cheaper to make them part of the trailers, which might remain in service for as long as 30 years.
Some early motorized rigs, like the 1929 Seagrave series hose wagons, had the bell mounted behind the cab. The men disliked this location as it rang in the officer's ear and literally made him tone deaf on a long run. Outside the cab on the officer's side was the standard (and favored) location on pumpers and hose wagons. Chief's cars had them mounted on the front of the vehicle.
Apparatus manufacturers used bells from different bell makers, each with distinctive tones. A knowledgeable buff could tell whether it was a Ward LaFrance, American LaFrance, Mack, or Ahrens Fox rig approaching merely by the sound of the bell.
The quality of the bells began to decline in the 1950's, probably as a cost factor. My opinion is that it was this decline as well as the air horn and radio communications that led to the disuse of the bells.
The CD pumpers had cheaper bells than the regular Wards of the time. The bells on the 1955 FWD wooden ladder trucks were awful. The worst were the 1959 (not 1958, which were just OK) Mack C95F series pumpers. It was smaller than anything before it. Mounted behind the bucket sets, it sounded like a tin can. My father was an officer at the time on one of those rigs and he just refused to use it. It was no longer needed returning to quarters as they were now on the radio, and he preferred the air horn (with siren) when responding.
By the War Years of the late 60's they just fell into disuse. By the 1970's they no longer came on the rigs from the manufacturer. Some companies still install them, more ornamental than anything else. L38 kept the bell from their last rig to come with one and have mounted it on each succeeding rig since. It is not used as a warning device.
At one time the sound of the bells, from the bell towers, to the telegraph bells, to the bells on the rigs, were synonymous with the FDNY. No more.