Having a cage in a bedroom is a bad idea in most situations (my opinion).
1) because people tend to do things carelessly if they can't see the bird's cage etc (e.g., burn food, use polishes, spray chemicals etc). The illusion that a door or even different floor is going to protect them should be avoided. No matter where the bird is located, no Teflon/PTFE/PFOA etc or harmful cleaners should be used anywhere in the home.
2) The bird is going to produce A LOT OF FINE/STICKY DUST (especially an african grey--A powder-down bird) and sleeping in the same room with that dust is not a good thing for either of you. You can get "bird keepers lung" if you breathe a lot of it (and there isn't much air flow in a bedroom). It also is bad for a bird to breathe its own dust in excess. An area with more air-flow is preferable. I slept in fairly close proximity to my cockatoo for a good length of time and I'm still alive, but it can be harmful (we never shared a bedroom, but my place was small and she was in the main room which was right outside of my bedroom--this was not the healthiest choice for either of us).
Currently, we are in a decently-sized 2 story house.. If I pull my elastic pants/leggings away from my leg and let them snap back against my body, a poof of visible dust comes out (even though my pants look black)!!! I am a clean person with a billion filters running, lots of sweeping/vacuuming and freshly laundered clothes---After one day of wearing these pants (most of which was spent at work) they poof repeatedly and it is disturbing lol...It is just crazy. Cockatoos are probably worse than greys, but they are both powder-down birds. When she puts her head on my chest and I am wearing a white shirt, it looks like someone with flour on their hands high-fived me there.
3). If you get sick, you could potentially pass on certain germs to your bird (and vice-versa) when sharing a sleep space. There are also certain things that birds can pass to humans and if you are cleaning the cage (as you will be) and the bird is pooping in it, then some of that dust (as well as the powder down) will be in your airspace--- it does get into everything.
4) Your bird will inevitably be shut off from certain activities if in your room (even if your intent is to keep him included). For instance, my bird has a fear of stairs and narrow hallways---if you start your bird in your room on another floor, they may be somewhat resistant to joining the rest of the house (depending on how social they are and how scared they are of random things). I would establish the safe-place (cage) in the social place, because that is where your bird will feel more comfortable and you don't want him/her to adjust to your bedroom initially during that "I won't step up" period that occurs with most parrots.
In an ideal world, I would have one cage for the main living room and another cage in a separate room (not an occupied bedroom though) for the bird to sleep in. I currently do not have this setup, but it is what I strive for. Instead, I have a very weird old house with a lot of rooms and doors on the first floor (which can be opened or shut). At night, I close the rooms to her door, but during the day, the doors are open so she can see me in most locations from there---plus, she has a stand perch in the room that separates her room from the kitchen.
Like I said, there was a time when I lived with her in a smaller space and my room was very near to her cage. That having been said, I am glad I didn't have her in there with me because the dust situation was insane (even with a purifier) and she sneezed a lot more there.
No matter where your bird is located, I would strongly suggest purchasing a high-quality air purifier (non- ionizing, or with an ionizing setting that can be shut off).
I recently "splurged" on quite a few (due to house changes) and I am very glad that I did...I had to get on a payment plan for the "Alen BreatheSmart HEPA Air Purifier for Allergies, Chemicals and Cooking Odors with a HEPA-FreshPlus filter" BUT the difference is NOTICEABLE and if I could go back, I wouldn't have wasted my time on cheaper models. I also bought 2 other smaller purifiers from a different company, but in a house, the dust gets into your hvac system and it helps to do whatever you can to minimize it. Look for a true hepa purifier that handles mold, dust, VOCs, etc and try to find something that covers as many square-feet as possible. Don't skimp on the filter, as it is the heart of any good system. I think mine was like $700 when all was said and done, BUT I only have to pay $50 something each month and the approval process for that plan was super easy.
5) rooms often do not provide much sunlight.
