I dont leave Darcy in the bath unless I need to grab her towel, but I can still see the bathroom from the airing cupboard so not as if I can't see her. She is only 23 months though so not as old as most of your LOs!
As for playing in different rooms, the only time we do this is when we are getting ready in the morning and we just leave her bedroom, our bedroom and bathroom doors open upstairs so she has free run and she usually spends most of the time following us round telling us what she is doing, or asking us what are we doing

Downstairs we have a stair gate on the living room door as we can't have one at the bottom of the stairs. Now she is getting a little older we aren't as worried about leaving the gate closed, but only if we are sitting in the living room so can hear what she is doing in the hall, my main worry is her getting out of the front door now she can reach the handle, so have to make sure door is locked and key is put up high at all times. If we have the doors open in to the dining room we dont mind her wandering in and out, but as soon as she goes through to the kitchen we give her a couple of minutes then go and ask her to come back in as we dont have locks on the cupboards and there are things in there that could be harmful. I think it really does depend on the child and how they would normally behave, there is always a first time for everything though so I have to say I tend to air on the side of caution