How about you get two of these type brackets (they come in a pair) and mount them to two adjacent studs but triangulate them together to a mount point for the punch bag to hang from.
These particular brackets are 24 inches in length and if triangulated as shown below on studs that at 16 inches on center you would achieve a projection from the wall of about 22 inches to the place you could hang the bag.
Several different techniques could be used to provide the mount point for the bag but the easiest may be to simply use the brackets up-side down and use the loop near the end on each bracket. Another way may be to bolt through the end with a good sized bolt with a couple of large washers. An S-hook or similar could be secured around the middle of this bolt.
You can place spacers behind the mounting flanges or bend them to be flat against the wall. It may be advisable to mount a piece of sturdy wood on the wall between the mounting flanges and the wall surface to bride between the studs and add strength. If you used a piece of 2x8 or 2x10 that was about 24 inches in length several additional advantages would be realized. One would be more projection and another it may allow you more flexibility of where locate the bag mount point of directly midway between studs was not ideal.
I found this particular pair of brackets at Amazon. They are probably available also at shelving stores.