As others have said, "Connect under reset" works for cases where you've used the debug pins for other purposes.
The "wrong value resistor" on the Blue-Pill is for the USB port, and it may work "as is" with some systems, however the point is a bit moot because IIRC the STM32F103C8T bootloader doesn't support USB.
Do you have a USB serial adapter providing RxD, TxD at 3v levels? If so, you can use that to access the on-board bootloader and it works fine on the Blue-Pill (done it many times!). If you don't already have such an adapter you probably want one, because using an on-chip USART is the simplest way to implement a debug console (very little code to talk to it).
Dave