Hang it from the ceiling:

Hettich TopLine 71-222 Standard Single Barn Door Hardware Kit | Wayfair · More Info

https://www.wayfair.com/home-improvement/pdp/hettich-topline-71-222-standard-single-barn-door-hardware-kit-hech1004.html

Thank you!! I didn’t think of this. Is there enough room on the left and right sides of the space for the doors to open and close? That’s another concern I had.

If you are renting get creative with furniture. There are shelving unit systems you could use that could create more privacy. Or the drapery on a tension rod. If you own then the ceiling mount barn door could work.

https://www.houzz.com/hznb/photos/room-divider-metal-frame-shelving-unit-contemporary-london-phvw-vp~142800281

Cheapest solution is to make your bed every morning :)

Will your landlord allow you to install a barn door?

Add an open shelving unit to the left side of the opening to block the view of the bed (if that is where you plan to keep the bed) and fill with lidded baskets for storage, books, etc. to partially block the view of the bed but still let light through.

Edit: yes, I did get permission to install the barn door provided that I remove it prior to leaving

Hi, it’s a big space. Not really a studio, but since there is no window in the bed area code probably doesn’t allow closing it off as a bedroom. I think a curtain is your best option.

I don't know how you'd be able to detail the barn door with the TV location (plugs/wires). After further thought I don't see how it would work.

What about a hinged, folding screen? You could buy plywood cut to the size you want the panels to be, paper it with travel or theater posters and then cover with clear varnish. That way you would not risk damage to the walls or ceiling of a rental and could easily keep it folded to the side when you don’t have company.

I like the idea of a folding screen the best ...you can make your own and display photos on one side ..or buy them ready made ..( Chinese screen ) ...or , a beautiful black velvet curtain ...open when at home ...closed with company .

Please do not install any kind of door for fire safety reasons! There is no other fire escape, no other exit, no windows, from your bedroom (which is why it's doorless, fire code wouldn't allow it).

Buy a bookcase or larger entertainment center, scoot it over to allow a 42" opening, and anchor it to the wall. Then install a curtain behind it.

It won't look tacky, will be much safer, and will get the privacy you want when guests are over.

I played around without knowing exact dimensions and used these items in the mock up:

Ikea TV Center

Amazon Privacy Curtain

You do not have the space for a barndoor the right size and the way your space shows the only time people will see the bedroom is when they walk by. Get some fab bedding a piece of great art on the wall facing the living spce and leave it open or maybe a skinny divider that just makes the entry a doorway size.You will curse a free standing screen every time you knock it over .This might work if you can attach to the door frame on one side.

Check this out: https://www.roomdividers.com/shoji-screens.html#/filter:ss_height:64:82/filter:ss_height:82:300
But you can also check out Etsy or google making your own, either with fabric stretched over a frame (might be lighter weight & give privacy without bulk), wallpaper or paint. Look for shoji screens, room dividers, etc. Picking the right fabric could get you the farmhouse look.

Consider an accordion-style folding door attached on one side. It doesn’t need to go all the way up to the top of the opening, so you still have air circulation. I would get rid of that silly too-tall uplight lamp unless you use it to observe a spiderweb in the upper ceiling corner or use it as a night-light with a dim bulb.

Some Decor Solutions Become Problems

"I did get permission to install the barn door provided that I remove it prior to leaving"

Not only would you need to remove it, but I'm certain you'd need to patch and repair the damage from the installation OR- lose your entire security deposit AND possibly incur more charges for damages. An installed door is not worth the trouble.

When I rented, I was excited to hear that I could paint the apartment, until I heard that I'd need to repaint it back to white when I lmove.