I couldn't tell you for sure if they fit your bike, as I've never owned a CB360 before. I googled it and it looks like the CB360 takes a 7/8" bar. I'd recommend looking it up in your manual if you have one, or measuring your existing bars or bracket. It should be fairly easy to tell. I believe the next size up is 1". I'd recommend you double check the required diameter then get back to me if you are still interested.
Thanks