one faucet smells

We are on city water here in Bismarck. Each time we open the faucet at the lav sink there is a sulfur smell and bad taste. Left to run a few seconds it clears up. Next time same thing. It only needs to sit a few minutes to "resmell." We just use a cup of water from the kitchen to rinse teeth, etc. That faucet is the only one this happens to. We've checked the shower and kitchen. No smell or taste. This has happened in other locations as well so it isn't the fine Bismarck water supply. Any ideas? I don't really want to "sanitize" the whole system if I don't have to.