So if you are sending the A-155 output to the CV input of the Bit Crusher that voltage would be used as the second source for the logic, That signal would get treated as a High/Low.
I've tried with a number of other sources (I don't own A-155) and can confirm the BC functionality works with a variety of signal voltages via oscilloscope. It has a pretty low threshold for hitting the HIGH value though sometimes you might not hear it. No need to manipulate the voltage +5 is plenty high.
Hear is what I *think* may be your problem. Between the inherent low sample rate of a bitcrusher and the very short change in input signal you likely won't hear much change. Here's why:
The A-155 is likely sending a GATE out signal nearly constantly (ie some not is always getting played) and the sample rate doesn't pick up the couple of ms time between notes. If you don't have any rests/note off the value of GATE only changes briefly during the switch... thus it always treated as 1 in the logic. Remember GATE is a HIGH/LOW not the value of the note.
With a Trigger signal you have the reverse problem - the signal is almost always low. I used a LFO sent to a Gate to Trigger converter to test. Only on a few different speeds is the change even noticeable audibly and just as a periodic crackle sound. (ie Trigger is nearly always treated as 0 in the logic)
The solution: Make sure the signal your sending has values both high and low values for long enough durations for the A-189-1 to sample it at opposite values. I am assuming you want to see variation/distortion rather than a simple downsample of your audio signal. A-160/161 produces noticeable changes because you have longer high/low signals.