First bit of advice... - Not knowing how much room is between the current ceiling and the roof of your home, I will remind you that you need to leave enough room on top of the new ceiling to add enough insulation to meet fire codes, and keep the home properly insulated and the attic/crawl space vented.
Around here (Illinois), we need an R-22 rating for ceiling/attic code... and an R-11 for exterior walls I personally prefer an R-25 or R-30 for my attic and R-20 for my exterior walls. This reduces my heating/cooling costs, but still allows my home the ability to breath. You don't want your home too well insulated, or you are asking for other problems, including personal health issues.
You will also want to take a "trip" up into the attic or crawl space above said bathroom before you start cutting. You may have electric, phone, cable, pipes, etc. up there that will need to be moved and rerouted before hand.