As far as I know; this requires, the use of a VW specific scan tool, that can do the output tests. I have bled the abs system successfully; I used the Ross Tech VCDS. If you don't want to spend the money or buy VCDS, you might be able to do the same thing with the $50 VAG 401 on amazon.com. I cannot vouch for the VAG 401; since, I have not used or own one but many forums online, claim it can do many of the same things as VCDS (note: documentation is poor and familiarity with VCDS would help).
Here is the procedure; from Ross Tech:
ABS Pump bleeding:
ABS Brake Pump Bleeding
Updated 13 Feb. 2012
Ross-Tech is not responsible for any damage or problems that may result from following these instructions. They are to be used at your own risk. These instructions apply to many older VW/Audi models but may not work with many newer ones. As always, you should refer to a Factory Repair Manual for your vehicle! Also check the Ross-Tech Wiki to see if there are vehicle-specific instructions that you should use instead.
This procedure details how to bleed the ABS pump when replacing brake fluid. This procedure is NOT necessary unless your ABS pump has gone completely dry. For normal brake work including fluid replacement, hose replacement, pad replacement, etc. this procedure is NOT necessary. Also, this procedure does not take the place of good ol' fashioned brake bleeding with one person operating the pedal while the other person opens the bleeder valves one by one and collects the discharged fluid.
There are certain test conditions that must be met before doing this procedure:
Vehicle must on a lift or safe jack stands with no wheels touching the ground
Ignition should be in the "On" position
Procedure for Bleeding the ABS Brake Pump in many older VW Golf, GTI, Jetta, and Audi TT with Mk20 or Mk60:
[Select]
[03 - ABS Brakes]
[Basic Settings - 04]
Group 001 (may be group 002 in Mk3 VW Golf/Jetta)
[Go!]
This will trigger the ABS pump to turn on for about 10 seconds. You should hear the fairly loud pump clicking during this time.
Click the [Done, Go Back] button and you're all set.
ABS Coding:
http://wiki.ross-tech.com/wiki/index.php/VW_New_Beetle/Cabriolet_(1C/1Y/9C)
Having said all of the above; WHY are you replacing the ABS unit and what is the problem with it?
Common issues:
1. the board fails; causing a ABS light and fault code. (these can be rebuilt; doesn't require removal of the pump but the just board, all hydraulics remain intact and no bleeding is required). Search online; for repair service providers: (e.g. BBA REMAN, etc.)
2. there was a VW recall, on some of the ABS controllers and could be fixed for free (call your local VW dealer and see if this applies to you).
In general; we have not had allot of members, need to replace the whole pump itself.
This repair process may be; beyond, the skills and VW scan tools, that your average owner would have. If in fact; you need to replace the ABS unit, you could replace it and have a pro code/bleed the system. You need to figure out; the costs and see if it is worth the time, money and effort to invest in the tools required to do the work.
NOTE: Brakes are NOT; something you want to play around with and because of the safety issues, you could be putting your LIFE on the line if things are not done correctly. While, most of the typical mechanical brake repairs are easy; the ABS system, does require some advanced factory vw level scan tools, programming, specific bleeding/scan tool procedures and knowledge, to repair successfully. If you feel; this is beyond your capabilities, you probably should leave ABS repairs to the professionals.