You love your car. Oh, do you love your car. But maybe it's time for a change. Nothing drastic; nothing expensive. Just the car equivalent of a manicure -- a new flash of color for your faithful friend. You're going to paint the brake calipers.
That pedestrian should not have stepped off the curb. Clearly, she doesn't see you. You hit the brakes, and she jumps back. Problem solved -- except that high squealing sound doesn't seem to be coming from the pedestrian. It's coming from your car.
If the term "bleeding brakes" conjures up images of a clean, contented person stepping on a brake pedal while another grumpy, dirty, frustrated person yells, "Push down!" from under the car, your image would be correct.