I think there are many posts on this and I have had this occur on a few occasions. I am pretty sure the answer that fits with most of these posts is an inflammation or strain of the bulbocavernous muscle muscle. I believe if you will carefully palpate (feel) this muscle, you will find it is a little more tender on the side that is 'buzzing.' This would also explain the occasional female that mentions a similar buzz in the clitoris. So, the bike riding, the sitting for long periods of time, the straining / lifting -- all these can cause you to strain this muscle. It also explains why the symptom went away in the individual that too a long hot bath -- it is like any muscle strain. That said, there are also other conditions that can put pressure in this muscle and as one of the physicians that posted said -- if it does not go away with in a week or two, seek additional medical advise.
I met with my doctor last week and he asked me if I had started any new exercise. I told him I was starting to train for a long bicycle ride (100 miles). He said this was a normal function due to the strain on the nerves and the muscles. He said it should go away in a couple weeks.. and .. he has been right. It has.
I have this as well, but on the right side. I noticed in another discussion that many people were mentioning this, but the discussion also mentioned vibrations in the head and things that sounded more like twitches or spasms. I think it would be nice to a get a response to the cell-phone like vibrating in the this location of the body since it seems to be quite common.
I also think doctors may not know what it is because cell phones are modern, and while it feels like a cell phone vibrating, in the the past people may not have called it a "vibration".