You said "I can't do that (can I?) if the Mini isn't connecting with IDE to burn a bootloader, though."
You need a Programmer to bootload a Mini. Not just a USB/Serial adapter as is pictured in an earlier post.
A Programmer connects to Power, Gnd, Reset, and SCK, MISO, MOSI to access/control the memory directly and load the bootloader.
Once installed, the bootloader then runs after a Reset and looks to see if download code messages are coming in from the serial interface and the Mini then copies the code into its own memory. If ino code download messages are seen, whatever sketch is loaded then runs.