The bathroom can be very easy to ig-proof: close the toilet, cover/remove the waste paper basket, close cabinets and put harsh cleaners away, and make sure the tub and sink drains are closed/covered, and you're set. Also make sure there's nothing on the edge of the tub that he can pull in onto himself or otherwise knock over.
It's a fun place for your iguana to play for beginner supervised play time; my iguana is about three and he still loves to climb up the towels on the towel rack, bob at the mirror, and climb in and out of the tub. If you close the door, you have a small inescapable room that can be made warm and moist very quickly (let the shower run hot for a few minutes before you go in, and my bathroom came equipped with a "heat lamp" for humans to dry off under), and you can just hang out with him and let him explore and get used to you.
Of course, it's going to be a lot more fun for your ig AND you if you ig proof other rooms in your house, too. But that's a good place to start. Just don't let him get near your family's toothbrushes or contact lens cases or anything, and disinfect if he poops anywhere.
Have fun!