Managed to get the Logic Analyzer working, I had to install firmware for the generic driver. I also had to install and enable udev rules so that the regular user has USB access.
Tested the logic analyzer by generating a 5 bit counter with an Arduino Uno, and I was able to detect the signal. I tried to connect the HC-05 and AT-09 serial Bluetooth boards to the logic analyzer, but I can only get the HC-05 and one AT-09 to pair with my phone. However only the HC-05 registers a connection when the State pin goes high. Typically the RX and TX pins are either always high or low, no matter the signals sent. Aside from possible mismatched baud rate, pin misconnections or the voltage divider on the RX pin is not correct so it is not triggering properly.