One thing I learned pretty quickly being a new mom at 19.... babies don't care if you need to shower. They sit in their own dirty diapers so if you smell, it doesn't phase them. And they seem to have the keen sense to know, even when they are completely and totally fast asleep, that you have JUST stepped in to the shower and under the water because that's when they wake up and they cry.
They aren't content to lay there and babble to themselves while you finish washing your hair, they want to be picked up and they want to be picked up NOW. Crap. Right?
I figured out the hard way that if I waited until they went to sleep, and I thought they were down for the count, before I went to take a shower... I'd never get clean. So what did I do? Put them in a bouncy seat. Bring them in the bathroom with you. Set them on the floor in it a foot or 2 away from the tub. Should they be able to stay in bed so you have some you time? Yes. After a while. But realistically... what's more important to you? Showering alone, wondering whether or not the baby is going to wake up and need you? Or just showering.
Really. Baby is in the bouncy. Or maybe a Johnny Jump Up in the door way (it's your house right? who says you have to have the door closed). And you're in the shower. Baby can see you. Heck, play peek a boo with the shower curtain. Wash your hair. Scrub down. And you're all set. You got clean, and baby didn't have to exercise their 6th sense and drag you out of the shower when you'd barely gotten your toes wet. Everyone is happy. Or at the very least... taken care of. :-)
You don't have to try and work around them.... work with them. Takes a lot less time.