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.

Good luck.

You also can't just cut out ceiling joists. They are holding up ceilings in the adjacent rooms. You need to head them off some how. Ther is a lot more to it than just cutting a hole and reframing it.

Thanks guys, I did check out the attic, (I'm an Electrician ) so there is no problem there. I would set 2x8 headers on the attic floor to head off the existing floor joists, then frame up from there.

Joed - Another point that I forgot to mention. Thanks for adding that in.

You not only need to be concerned about insulation a vapour bariers but structural framing. If the house is roof framed with trusses you will create a disaster. If the ceiling joists are also important rafter ties, the ridge will eventually sag.