A good friend of mine is a jeweler. He said to get an empty medicine bottle, fill it with warm soapy (I use dawn liquid dish soap) water, put the ring in it, close the bottle, and just kind of easily shake it for a minute or two...maybe even let the ring sit in the water for a while. After wards, get a soft bristle toothbrush and just kind of go over it. Repeat if needed.
This process really really helps clean my ring.
Also, I WOULD NEVER drop my ring off to have it cleaned. Anything could happen to it. Many times I have literally walked in to a jewelry store and asked to have it quickly cleaned. I waited as they did it. Go in during an off-time and I'm sure they will accommodate you.