ATtiny85. How do I burn a bootloader? What is the process?
Yes, there are USB interfaces for ATtiny85. Just look at one of the open hardware designs out there, e.g. Digispark.
An USB interface is going to require two pins, so using one to save one pin doesn’t strike me as cost effective.
I agree with @FAD, that you don’t really need an USB stack, and simply could do a time-delay-at-boot thing with the UART pins.
HVSP (the high voltage programming) is not hard to do. If you’re already comfortable with ArduinoISP, you can try ScratchMonkey, which uses the same approach (with a 12V power supply and one transistor) to do HVSP programming.