The water pump comes on every time a faucet in the house is opened.

You don't need to bleed it, but you do need to check your pressure tank. You have the classic symptom of a waterlogged tank. Next time you turn on water, watch the pressure gauge. It will likely drop 20 psi in just a second or two. If that is the case, look for an air valve at the top of the pressure tank. Press the valve for several seconds. If water comes out, then you have found your problem. In most cases, it is time for a new tank.

There is a "get-by" in case you need to make it for a few months without a new tank. That is assuming that a new tank if called for.

It is also possible you are dealing with a booster pump, in which case it is behaving as it is designed to do.