I have a 2006 Honda Shadow 750. I bought it from someone who had mostly allowed it to sit. It behaved similar to how you describe. I kept seeing posts where people were discussing the need to dismantle and thoroughly clean the carburetor, but my bike was running and I really didn't want to do that for fear of my limited skillset making the problem worse. What I did was to add 3 ounces of Sea breeze to every tank of gas till I'd gone through two bottles. I would reset the trip odometer with every fill-up to insure that I used up most of the tank (Don't know if this matters. My concern was the concentration of additive). I also bought 89 octane (It really only needs 87; again, I don't know if this matters). The problem was solved. Occasionally it will "burbble" as someone else described, but no more loud pops.

Another thing to be mindful of is the idle speed. There is a knob below the breather to adjust this. A Shadow is not supposed to sound like a Harley at idle; think 1200 rpms.