UPDATE TO MY PREVIOUS POST
I realize that this thread is very old but I wanted to correct a couple things I wrote previously and add some current information.
I should have mentioned that you bleed BOTH the front and rear ABS systems, not just the rear. That should be obvious. Reviewing the procedure in the factory service manual, I noticed that Triumph says that bleeding the ABS systems is only necessary if the ABS module has been replaced or otherwise drained. If that's true, it would mean that ABS bleeding isn't necessary normally and that the system is "open." In other words, brake fluid passed throught it during normal braking.
Also, TuneEcu now had a tool to bleed ABS. I don't know about the old version that ran on laptops or PCs, but the new version of TuneECU that only runs on Android phones does have a tool to bleed ABS.
Also, I should have mentioned more about the ABS bleeding proceedure. (There's at least one YouTube video showing how to run it with TuneECU.) Triumph says to have someone press the brake lever (front or back depending on which brakes your bleeding - they're completely separate systems) while the bleeding tool is running. The bleed screw must be open, of course, while bleeding. When the ABS bleeding program stops, have the helper continue to hold down the brake lever while you close the bleeder screw. Some sources (not Triumph) say that if you run the tool more than once on the front or back brakes, allow about 10 minutes between running the tool so the ABS module doesn't overheat. Triumph doesn't mention that but I thought I'd mention it. It couldn't hurt to do that. But remember that Triumph is talking about using their too, not TuneECU or DealerTool. (I bled my R3T brakes with DealerTool in the past but I always found it to be very difficult to get DealerTool to work. That said, the DealerTool folks have always been extremely helpful and got back to me via email very quickly. Even so, I almost dread using DealerToo, not because it doesn't work well but messing with drivers, etc., has always made it hard to connect to the bike. In fact, the last time I needed help from DealerTool folks, they sent me the list of steps I should do to get it to work. It was two detailed pages!
One more thing: If you have the factory service manual for your Rocket III (not the 2500 CC models), either the hard copy (which I have) or the free online downloadable version (which I also have), and you're looking in the brake section for information about ABS and don't find it, know that there's a large added section to the manual that covers ABS and all kinds of other things that changed or were added since the manual was issued. You can download the official Triumph factory service manual for free here:
TRIUMPH ROCKET III OWNER'S HANDBOOK MANUAL Pdf Download