CrossRoads:
A pair of TPIC6C595 can drive 8 bicolor LEDs. You can daisy chain as many as you want, I've done up to 45, with the Arduino driving 5 74HC125s, and the 125s then driving 9 each of the 595s. 8 x 45 = 360 LEDs, well I guess 180 in this application.
@CrossRoads - I have been looking at the 74HC125 and don't fully understand their purpose in this scenario. The are a quadruple bus buffer and seem to be commonly used for logic level shifting between 3.3v and 5v. I don't think that's the reason you suggested their use though. Are you using them to 'boost' the serial signal on the board due to trace length ? Or does it have something to do with the tri-state capability of the IC ? Are you using these on an SPI bus ? How did you come to the number of 1 x 74HC125 for 5 x TPIC6C595 ? Please excuse my ignorance !