I just read several articles on the subject. If it is just one faucet and cold water only there were a batch of Moen faucets that were released with the wrong type of plastic tubing inside. Moen will ship a repair kit if you have that faucet. If it isn't a Moen, and still cold water only from one sink, there is a possibility if it is an older house built with galvanized pipe, that the plumber used a cutting oil to thread the pipe that contained a sulfur base. If this is the case it can only be repaired by removing the galvanized pipe and replacing with plastic or copper.
Now you could have an issue with a clogged trap as well and decaying hair. That's the most quick check of all. If the sink does not drain quickly, pull the P Trap and clean it, put it back together, and then run some draino through it so it etches any surfer oxide bacteria that may remain away.
If it is the Hot water, your best bet is as spoken earlier. The Anode in the hot water heater could be the problem. However if this is the case your issue will show up at every tap to some extent. Just changing the anode isn't the complete cure either. See if there is an aluminum replacement for your water heater model. They don't last as long, but they create much less Hydrogen Sulfide, which may be what you smell. NOT Sulfur Dioxide. If it is Sulfur Hydroxide be very careful about your working conditions. Be sure you have plenty of air flow, and no fire, arc, or sparks going on when you replace the anode and flush the hot water heater. Sulfur Hydroxide is deadly, and extremely explosive, and is heavier than air. It will sink to the lowest point and collect, one match or lighter and BOOM. This normally occurs in well water situations, but can occur in a hot water heater with a magnesium Anode.
See: http://en.wikipedia.org/w/index.php?title=Special:Book&bookcmd=download&coll ection_id=10a4aadf6b81101f&writer=rl&return_to=Hyd rogen+sulfide
And also: http://www.mrwa.com/watersmellrotteneggs.htm
The other thing you will want to do after the anode is replaced and the tank is full, is to set the heat to 165 degrees for about six hours. This will kill any remaining Sulfur bacteria that may be in the tank on the walls. BE CAREFUL NOT TO SCALD YOURSELF During THIS PROCESS! After this process you will want to turn down the thermostat, way down and run the water for a long while. Once cool enough it is a good idea to completely drain the tank again, and flush it out. Then cork it back up, reset the thermostat, and your good to go.
If you are on a well, you probably need to ‚ÄúShock‚ÄĚ the well. This can be a simple procedure if the parts per million are not too high. You should have a well log book that shows when the well was last shocked. A well that is emitting sulfur smells should be shocked about once every one or two years. Shocking a well involves opening the inspection cap at the well head, sometimes a cap on a pipe standing up from a T on the out bound supply line, or the well casing and dumping a gallon a bleach down the well. Let it sit for about an hour then run the tap that is the farthest away from the well for a good two hours to clear all the dead bacteria, and bleach from the system. The chlorine in the bleach kills the sulfur bacteria.
If you have a well and the smell is bad, it is a must to have your water quality tested by a reputable LAB. Most States have a Department of Environment Quality some Cities or Municipalities have a Water and Sewer department that can do the testing for a small fee. You may have more going on in that hole than just Sulfur bacteria. The lab can tell you exactly what is in the water, and what to do to clean it up, if it can be cleaned up.
Start with the simple things, check the trap, check the faucet, look in the basement or crawl space to see if the supply line is galvanized. All simple things you can do to create a process of elimination. But above all, if the smell is bad enough you can't stand to be in the room, you need to have the water checked by a LAB.
If the problem is the generation of Hydrogen Sulfide, it will smell for a few min. and then seem to get better, as it deadens your sense of smell, at that point it is building up in the wash basin and soon the room. This can lead to serious injury or death. Get it checked by a professional and make sure you tell them exactly what you have checked and done, and you suspect that you may have an issue with Hydrogen Sulfide. Don't try to go cheap and fix it yourself. Some situations can be deadly if the gas is allowed to build up and you are not wearing a SCBA (Self-Contained Breathing Apparatus) similar to that of a fire fighter. Professionals can test the water and the air quality, you cant.