Have a look at the following image:
That's a rough idea of what the voltage at the capacitor looks like in a full wave bridge rectified system. (Once it reaches an equilibrium state.) The grey curve is supposed to show the rectified DC out of the bridge, but this will actually be about two diode drops lower and there will be a tiny gap around 180 degrees and 360 degrees, and so on. But it's close. The main point here is that the thick black line shows you what the capacitor voltage roughly looks like when there is a real load applied and the capacitor is designed within some range of reason for the load.
As the rectified voltage gets past the bridge and is rising, at first it does nothing much since the capacitor voltage is higher. But the capacitor is still supplying current to the load and drooping, so eventually the drooping capacitor voltage and the rising rectified voltage cross over sufficiently to forward bias the diodes in the bridge and the capacitor voltage follows the rising voltage (or what remains of it, this first half of the first half cycle.) For this very short time before the bridge voltage peaks, some few degrees before 90 degrees, the transformer/bridge system is supplying current to the load and the capacitor.
As the rectified voltage rapidly declines and falls away from its peak at 90 degrees, it also falls away from the capacitor voltage and the capacitor is then supplying all of the current to the load. It must continue to do this until the next half cycle, usually not much but somewhere before 270 degrees when the transformer/bridge system supplies all the current again.
That lowest point in the droop of voltage must still be sufficiently high for the following voltage regulator system (if there is one.) Note that if the load draws more current than before, then the slope of this droop will steepen and it will dip still further down before the rising voltage from the bridge rectifier catches back up. Also, if you use a smaller capacitor even if the load current stays the same, the slope also steepens. So you need to make sure your capacitor and expected worst case load match up with the needs of the minimum input voltage for your following regulator system.
As you might guess, by now, there is no simple, linear, one-equation-solves-all-problems here. Some thinking is required.