Part of me wants to simply answer "You're overthinking this", but... you know what? I'll post a logistical answer instead.
So, first up: take a look at how you're arranging your furniture. Keep in mind, you can move your work desk to wherever you need. Maybe you've got it flat against the middle of the wall, and it looks straight out along the middle of your studio apartment. What about putting it flush against the corner and only letting the camera capture one half/side of the apartment? What about putting it next to the bed itself? Or for that matter, what about rotating the desk 180 degrees and offsetting it from the wall, so that you're sitting in a mini-cubicle and all the camera could capture is you and the wall behind you? Keep in mind, you have all the power in the world when it comes to organizing where stuff resides in your apartment. If something isn't working for you, brainstorm ways you could reorganize to improve!
Second, have you thought about getting a USB webcam and using that as a source (I assume you're using a built-in one on a laptop.) If you do it that way, you can have the webcam capture you from a different angle than face-on from the screen - which will let you have more control over what angle of shot is your backdrop. Between this and putting your desk in a corner, you can easily have your 'backdrop' simply be the wall to your side.
Third, have you considered going professional with the bed decor? Do a google image search for 'Studio Apartment', and you'll find result after result that look pristine, immaculate... and, well, wouldn't be bad for a backdrop. In other words, instead of fighting to keep a bed out of frame, add 'making the bed' to your daily morning routine and make it something that wouldn't be bad to have in frame.
I mean, I can't imagine someone thinking bad about this as a background: