Kimberly, if you will add more pics of the entire wall & room to show style of furnishings, the Pros on this site may offer specific ideas for “ outside of bay window” treatments. I can only offer that I know there are options but I can’t suggest any as they could!

Here are the pics

It is a lovely window. A real statement! Treat it as such! I'd hang a rod just under the ceiling, extending beyond the window trim on each side. a subtle textured panel with a large size rod. Rods are available in so many great options, Polished, Dark, Pewter, whatever your style. if the natural light on the middle window isn't an issue, I'd leave it uncovered. On the lower window I would install x4 Inset bamboo blinds top down/bottom up Blinds.com (come in a variety of colors from white to all sorts of natural tones)

Your home is beautiful. When I saw your doors, I was reminded of old country homes in England where draperies are installed between rooms to control drafts. Heavy (or in your case beautiful linen!) draperies on rings that can be easily swept across the space to stop drafts (or in your case, the hot sun.). It is a very chic way of dealing with the issues of old, elegant homes and, I think, would look wonderful in your home. Yes to a black metal rod between the door and the ceiling. A neutral linen….beautiful. Loose, elegant, yet modern.