Good question! The index finger is definitely what should be guiding the bow back and forth. Take a look at this video to get the motion of the index finger.
While you are playing the wrist is very flexible and adjusts to where you are at in the bow stroke. Here is a video that explains what the wrist should be doing and includes a good drill.
All your other fingers should be relaxed including the pinkie which should be flexible on the stick. You shouldn’t press with it as it causes unwanted bow tension. Take a look at this pinky drill video to understand what the pinkie does in the stroke.