Disclosed herein are bias voltage generating circuits configured for switching power supplies, and associated control methods. In one embodiment, a bias voltage generating circuit can include: (i) a first control circuit configured to compare a drain-source voltage of a switch against a bias voltage; (ii) a capacitor, with the bias voltage across the capacitor; (iii) a second control circuit configured to control the switch, and that is enabled when the bias voltage is at least as high as an expected bias voltage; (iv) the first control circuit being configured to control the capacitor to charge when the drain-source voltage of the switch is greater than the bias voltage; and (v) the bias voltage being less than an overvoltage protection voltage when the capacitor charges, and where the overvoltage protection voltage comprises a voltage that is a predetermined amount higher than the expected bias voltage.