Is the opening a stock door size? If so I would just have it cased & add a proper door. Will take a little extra work around the base moldings, however it should be well worth it.

Also you may need to have it swing into the bedroom instead of into the bath. You could even have a door made into two pieces as in a double door just to fit the opening.

I have no idea where builders or architects ever thought that homeowners would ever want an open bath. It is quite pagan!

We had the same conundrum in a rental master suite. Only the door was a 9 foot arch! I put an oil rubbed bronze rod almost to the ceiling then bought a tab top microfibre curtain panel that was 96 inches long and just pulled it to the side; the bath was compartmentalized but there was a 6' x 6' glass block window that allowed the bright desert moonlight to shine in and make the bedroom really bright at night. It was just different, but the curtain was heavy enough that it worked just fine. I know it isn't ideal but it did the trick for less than 50 dollars and an hours work of hanging the rod.

No to the sliding barn door. A fitted, frosted glass door would be airy, not block light but provide some cozy privacy.

Oh, and if light is a problem, dimmers are a simple alternative!

Bi-fold doors?