Controlling a Giant LED Dot Matrix Sign through RS-485

This looks like a signal from a floating bus. Is that bus in a defined state (using pull-up/-down resistors for A and B)? The number of resistors on that RS-485 converter would lead to assume it should have these in place. Do you have schematics for that board?

According to your wiring description RO is not connected. Please post a wiring diagram (may be hand drawn) of your setup.