Wheel speed sensors in the hubs are the most common failure causing the service stability soon message, but there can be several other causes, including yaw sensor, steering wheel position sensor, faulty EBCM and others. I wouldn't spend money replacing wheel bearings to fix this unless there are other symptoms of failing wheel bearings, such as side to side and up to down play in the wheel (when jacked up) and/or noises coming from the bearings when turning.
The best thing to do is get the car scanned with a system capable of reading body codes. Typically that is a Tech II scanner at the dealer, but there are several other sytems that can read these codes. If the shop you went to has a proper scanner, chances are your EBCM is the problem. These are expensive, but you can often pick up a good used one at Morad. If you do, you need the part numbers off yours, because each year has several versions depending on option content. Changing the EBCM is a very easy fix, and is done by jacking the car up, removing the front left tire, and removing the plastic fender liner. This gives direct access to the EBCM. 4 torx screws, open the electrical connector latch, and that'* all she wrote. The EBCM is dry, so you don't have to worry about brake fluid.
2001 Bonneville SSEi (retired at 365,000 Kms.)
2014 Jeep Grand Cherokee Overland (yes, I know its not a GM)