I had a lot of trouble bleeding the brakes on my 2001 BMW R1150GS recently. Turns out it’s mostly because I was looking at procedures for the newer R1150GS with ABS III. The older R1150GS has the ABS system from the R110GS (ABS II). Turns out bleeding this system is pretty straight forward. It can be done like most non-ABS systems. It’s a lot easier if you bleed from the ABS unit under the gas tank and then from the calipers. I used a vacuum pump to help get started. Bleeding by hand was still required, but I only had to pump the brakes a few times manually.
Here’s a video with some additional tips: https://youtu.be/WxG38nTWtPE