I would paint out the wood frame to white and maybe do a black out roman shade or even a roller shade. A sheer isn’t going to offer any privacy. Where is the toilet and shower? Can they be seen from the bathroom? Because if you’re concerned only about the tub I wouldn’t because what are the chances people will be outside if you’re entertaining and inside taking a bath at the sad time lol.

the toilet is on the left around the door , so your facing the window. It's more about the toilet privacy then the bathtub privacy

I'm planning a bathroom remodel and will face a similar dilemma once it and the deck are done. I would definitely paint the window and frame white to match the vanity. Is your deck floor the same height as the interior floor, or could you get away with a cafe curtain to leave you a view of the trees? A top-down/bottom-up shade is another idea.

thanks for your ideas. I also definitely feel painting out the window frame is the best way to go. I also like the idea of a blind going from bottom to top and leaving the view of the trees. My deck is same height as the bathroom floor. Thanks for the ideas. It's my first time putting out a post, so much appreciate the prompt response and thoughts.

Looks like the window trim matches your door and door trim in the room. I would not paint it white. It's beautiful with your floors.