BLE SPI Module with ATtiny85
I find the ATTiny85 working well with software serial port. Serial UART (or in fact any of the protocols like I2C or SPI) are just bit banging - and you can do that pretty well in software. Of course, having a hardware support makes things easier and faster, but there is nothing badly wrong with a software uart either. Except that you have to continuously check if there is some data arrives. 

I was using software serial on Adafruit Trinket (ATTiny85) in various projects to talk to a Bluetooth 2.1 module, and it worked pretty well.

Here
http://arduining.com/category/trinket-projects/ they use the same approach to talk to an ESP8266.

You may wish to look for the SoftwareSerial lib for Trinket, or in certain cases you may want to go for the SendOnlySoftwareSerial lib (send only, but smaller code footprint).

Also a hardware based serial lib is available:
https://blog.adafruit.com/2013/09/30/hardware-serial-library-for-the-trinket/