Is this an above ground jet pump, or submersible?? This problem is more common with a jet pump. Air leaking into pump housing, or bad / dirty foot valve at well bottom.
The bladder is like a balloon inside the tank that has a tire valve on top to set the pressure. This air pressure is what pushes the water out, until the water pressure at the switch is low enough to turn the pump on. When the bladder breaks, the solid water without the air cushion calls for the pump to run as soon as water is turned on, and will turn off when faucet is shut off. So the primary reason for the bladder is fewer, but longer pump cycles.
So pressure could be a lot of things. Bad switch, or clogged pipe to switch, or (If a deep well submersible) a wire going down the well to the pump is chaffed against the casing, or cut off. Each time the pump cycles, it tries to twist the opposite direction the rotor turns. There should be anti-torque boots like rubber snubbers to prevent the pump and line from twisting and thrashing against the well casing or rock sides. One wire cut off can allow the pump to run on 110 volts with only one feed wire. Not good for pump. Removing the pump switch cover, and running water to turn on the switch should show a spark at each (2) terminal point on the switch. If only one contact sparks, the entire load is on one leg of the two 110 wires going to the pump. This causes the pump to run slow, overheat, and not always trip a breaker.