You just need a motion sensor. Set the sensor to stay on alert for a few minutes, a longer period for a room you’ll be stationary in. Every time motion is detected it’ll reset it’s countdown and if you get it right you’ll avoid the lights going out and needing to wave at the sensor while you’re in there.
The bridge needs to be in the home app, but the room doesn’t matter. The specific bulbs will want to be assigned to their room. I don’t think the room in the hue app and the home app have to match (they don’t with the Ikea Tradfi system).
Some people create a fictitious room to hide all their bridges in. I like to keep them in the room they physically live in just so the virtual representation of the room matches reality.