I've had a mustache for 13 years or so. If you dont want it to be gross, keep it off your lip. I keep a small pair of scissors in the bathroom mirror thing and trim it when I feel it start to migrate too closely to my mouth.
Other than that, if you have a pointy nose like I do, water will cascade down the sides and seemingly miss your mustache altogether in the shower. I actually do have to consciously take some body wash and smear it across the top of my lip and chin.
I'm currently sitting here sipping on some captain morgan private stock, which tastes like liquid candy...kinda early, but I'm just gonna sit here all day anyway.