Is it possible to burn a bootloader to an ATTiny85 with USB TTL and avrdude?
No, you can't because a USB -> TTL serial device is not made for that. You CAN however use an Arduino Uno to burn a bootloader to another Atmel micro, including the Attiny85.

Now you may ask, can you use the Digispark in place of the Uno (and thus burn more Attiny chips). The answer is a qualified yes.  Another Arduino can do this -- search the web and find many examples. 

You might (?) even adapt that sketch from the Uno to the Digispark (saving the cost of an Uno). I can't advise further and you're looking at a rabbit hole of possible issues. 

Sparkfun does sell a chip which can perform boot-loading using minimal components:
https://learn.sparkfun.com/tutorials/how-to-install-an-attiny-bootloader-with-virtual-usb