How can I change the finish on my shower doors?

Yes you can!! This Hometalker did it too: http://www.hometalk.com/diy/bathroom/showers-tubs/turn-a-brass-shower-into-oil-rubbed-bronze-10288900?expand_all_questions=1

Although its been negatively stated,you can use painters tape to block areas not to be painted and spray paint them with a metal spray paint by Rustoleum.

Thanks Janet.

I think the designer Lisa Laporta used chrome spray paint on an episode of Designed to sell. It seems to me she used it on a range hood and a shower frame, and said it looked like brushed nickel or stainless steel...it wasn't super shiny like chrome. I have used a stainless look rust paint on a dishwasher years ago, that I rolled on. If you go that route, don't keep rolling back and forth like I did...It caused fish eyes/bubbles that didn't go away. That was when I was too impatient to let paint dry properly before recoating.

These links looks helpful:

http://www.blesserhouse.com/2015/02/how-not-to-paint-shower-door-and-how-to.html

http://simpledetailsblog.blogspot.ca/2013/03/painted-faucets-shower-enclosure.html

FYI Brass is back. Perhaps you could sand it to make it look brushed and it wouldn't be so shiny and "in your face". I am afraid whatever you paint on is going to scratch or chip off, especially with the high humidity and constant use.