If it seems like some kind of magic happens to your voice when you step into a steamy bathroom, that's because bathrooms do have some pretty wonderful acoustic properties. So you really do sound better to yourself when you sing in them!
Think of your shower as your own personal sound booth. The secret is in the construction. Most showers are made with smooth hard surfaces like ceramic tiles, which absorb next to no sound. When your voice isn't absorbed, it bounces around quite a bit, thanks to the close proximity of the ceramic shower walls. All that back-and-forth adds up, giving your voice more power and volume. When sound waves hit them, they're reflected back at you rather than absorbed or dispersed and the reflected sound amplifies your voice basically cranking up the volume.
This effect called reverberation, gives you the impression that the note you sang, lasted a little longer than you actually held it. Meaning your voice "hangs" in the air longer than usual, giving it an embellished, extra-rich sound.
Reverb also helps to even out your pitch, smoothing out the transition between notes which is great for those of us who aren't Beyonce.. Your voice tends to get blurry as it reverberates off many surfaces, so even if you don't quite hit the exact note, it sounds closer than it would outside the shower. So it's not as noticeable when you're off-key. A lot of karaoke microphones are actually designed to take advantage of this by adding reverberation electronically. Isn't that nice of them to make sure you don't completely embarrass yourself on stage!
The acoustics in the shower are so good that recording artists sometimes use them to record in. Weird Al's first hit single My Bellona, was recorded in a bath and the Pixies dragged their equipment into the studio bathroom to get the perfect sound for Where's My Mind and Gigantic. Apparently the Beatles also recorded quite a few songs in the bathroom.
So, go take a shower and sing your heart out!