There are many ways to strengthen your violin bow hold. One of them is just playing the violin with a proper bow hold.
Here are a few exercises you can do to help your development along.
We're going to cover 4 different violin bow hold strengthening exercises.
Finger taps: Using the pencil bow hold, tap each finger several times against the pencil.
Pinky taps: This is useful for placing your pinky finger accurately. Set your bow hold at the frog, and point the bow so the tip is towards the ceiling. Tap your pinky slowly and repetitively for 1-2 minutes. Make sure the pinky stays curled throughout the entire exercise.
Windshield Wipers: Set your bow hold at the frog, and point the bow so the tip is towards the ceiling. Slowly turn your wrist so the bow hair is facing towards the ground and the bow is horizontal. Rotate your wrist the other direction so the hair points towards the ceiling. Move just like a windshield wiper!
Pencil See Saw: Hold the pencil as you would hold a violin bow. Lift your pinky in the air. As you lift the pinky, push the index finger into the pencil. When dropping the pinky back onto the pencil, lift the index finger in the air. Alternate between these two motions, just like a see-saw, to feel the transfer of balance from one finger to the other.