Is it possible to talk with Attiny85 via serial interface?
For this simple task you can use a software UART like Here is an example. 

SPI is rather unusual to use with a PC and makes control software more complicated and I understand you don't want that. 

Not sure why you use USB to serial,you don't have an RS232 port or you find it"s TTL output handy.   If you have an RS232 port on your PC  you can use-it with some simple resistor level translator and inverting the RX input.