I think I'd rather stay dirty.

The worst place to be caught in a zombie invasion would be in the middle of a shower.  First of all, you're in a tiny room, generally one with no, or very small, windows, so you're essential trapped, and one can only do so much with a plunger or toilet brush, and unless you have a straight razor, there isn't much to use to fight with, unless the zombie is deathly afraid of spearmint.  Second, you'll be wet, and while that might seem like an advantage in that you'd be slippery and the zombie would have trouble catching you, it also might mean that you could slip and fall, or be caught and slip out only to crash into the wall.  Basically, it seems like a good way to prolong the suffering rather than shorten, or avoid it.  Third, you're not going to be wearing any clothes, and while that fact might not matter initially, later, like less than a minute after you're safe, you'll probably become pretty self-conscious about it, and since you were just attacked by a zombie it isn't like you can just pop into the bedroom and get some decent attire.  Nope, you'll pretty much be stuck in your birthday suit.  You might have time to grab a coat on the way out, but honestly, how many people have long coats just sitting by the door?  Then there's the weather.  It could be cold, but it's not like you could stay in the house, what with a zombie in there and all, unless you've left a baseball or cricket bat right outside the door and all you need to do is to get to it and get rid of the zombie, but really, why wouldn't you have taken it into the bathroom with you?  Even if you did, though, bathrooms can be tight, so you might not be able to get a good swing off, which means that you still might end up zombie chow.  I guess really the only way to get cleaned up, if that's what you want, though I'm still a little torn about whether zombies have a good sense of smell, or are attracted to the scent of spring flowers or melon, is to employ the buddy system and have someone guard the door.  That way, if the zombie does attack, they'll either get the person on the other side of the door first, and maybe, just maybe, that person will be enough and the zombie will shamble off with a full tummy to someplace else, or they'll be dead.  Either way, you'll be clean.  If that's what you really want.