The Adafruit Trinket Pro has the availability to do Serial where the base Trinket does not, at least not with out a software hack. The IR transmitter goes on pin 13 by default in the code. I attached a JST header to the Trinket so it could be powered off of a lipo. The one pictured is a bit overkill, but does the job.
The HC-05 Talks to the Trinket Pro over Serial using pins 1 and 2 on the Adafruit Trinket Pro and making sure to send RX to TX and visa versa.
The app made in app inventor looks like the picture below. Adding images and buttons is pretty simple. The toughest part is setting up the Bluetooth Client and list picker. Directions for that can be found here.