Check your wiring. Is it properly grounded or sitting in water with loose connections?
If there is debris in the pump itself (the rotating vanes) that may overload it too, although very unlikely.
I would check for loose, wet, corroded, badly grounded wires.
Too little electrical resistance would cause the circuit breaker to pop out. As stated, your bilge pump is probably singing it's swan song, but you should check the wiring to make sure there is not a short circuit somewhere. The bad part would be if you replaced the pump and still had the circuit breaker problem. . .
...most bilge pumps that I have encountered are induction type motors; even a locked rotor should not draw sufficient current to trip the breaker. I highly suspect a faulty connection or wiring.