There are 2 different scenarios that occur. One is a circulating current that can occur, mostly through the fact that the rotor is not perfectly formed (you can think of it as not being perfectly round) which creates a circulating current. Insulating one bearing will stop this circulation. The second scenario occurs when a motor is on a VFD (variable frequency drive) and especially a PWM VFD. This produces a charge on the rotor which wants to discharge, and the easiest path is almost always through the bearings. In this case you want to insulate both bearings. If you don't you will get even more discharge through the bearing that you did not insulate. In hazardous duty applications this is the way to go. In none hazardous applications a grounding brush or ring may be used as well. For VFD applications it is important that the rotor be electrically isolated from the driven equipment. If that is not done then the driven equipment bearings will discharge and then they will fail from electrical routing.
The purpose of insulated bearing for Motors with VFD drives or the Alternators is to prevent the flow of circulating current in a closed circuit through bearing and ground (if bearing is not insulated) and consequently prevent the bearing from damage.
This circulating current is caused by induced voltage in the shaft because of AC flux. Therefore, this voltage should be given a ground path by providing a earthed carbon brush on the Drive side of the bearing so that the voltage is not allowed to build up to a level that it can puncture the bearing insulation.
By using a common mode filter, which is a special nano crystalline magnetic core installed around the 3 wires of the inverter output (without the ground wire) a very effective mitigation is obtained. The best method for mitigating bearing currents is to use hybrid bearings in both ends of the motor, as insulated bearings (in both ends) is often not enough to withstand the capacitive bearing currents introduced by a VFD. Insulated bearings are unfortunately often very costly compared to a rather similar performance using common mode chokes. A brush can also be effective, but it is a wearing part which requires maintenance.