Let us get this out of the way:
There is not a single exercise on the planet that will make your bunion go away. The only thing that will make your bunion go away is surgery via a Podiatrist. However, there are exercises that can make your bunion less painful.
The exercise that I recommend for bunion sufferers is the Belt stretching exercises for Bunions. This will help place your joint into a relaxed position and help take pressure off the bursa. This will also help strengthen the ligaments on the lateral side of the joint as well as strengthen the abductor hallux muscle.
Here is a video of what the exercise should look like:
https://www.youtube.com/watch?v=GncdLDamLMI
Here is an inexpensive belt you can purchase from Amazon: