I’ve been looking at the same for a square bay window, such an awkward shape. Saw that you can get a curtain runner that could run right round the window. Possibly a solution?
Attached a pic from Pinterest

Lucky guests, what a lovely room with a great outlook!
Agree that the look of the window would be significantly improved by painting the frames and sill white.
The window is quite tricky to dress for a number of reasons: the deep sill, the position of the cupboard on the left, and not least the ceiling immediately over the bay that makes it very difficult to position a curtain rail that would look satisfactory.
I think that the simplest, most effective and best looking solution would be 5 roller blinds. That’s an economical solution too if you fit ready-mades yourself. They are generally quite easy to cut to size, and not difficult to fit - although in a bay the job requires a little patience!

I have a large box bay window with a wide sill. Like you, I looked at so many options. Shutters were too expensive, the window is 12’! Roman Blinds were also very expensive, although my friend has them and they do look very smart. I finally settled for made to measure curtains from Laura Ashley. They sit on the window sill. We had a new, strong white metal rail fitted by a local curtain company. Curtains were about £550 and the rail was £200 including fitting.

I have a bay window too and the last couple of curtains I’ve had have been to the floor. You can buy a pole that goes around the corner and then have passing rings to hang the curtains on that pass over the brackets. They go around the corner so there’s no gap at the edge. Here’s mine

Thank you all for commenting and for sharing some fab ideas. I think we have decided to go with a ceiling fixed, flexible track and some classy sill length curtains, similar to Sonia’s suggestion. Thanks again!

Just a warning if you have a track attached to the bay ceiling. It looks like the bay ceiling stops at the edge of the window, and so, because of the angles, there’s unlikely to be much, if any, wall space either side of the window to draw the curtains back onto.

Looking more closely at how the tops of your windows meet the bay ceiling - I fear that if you run a track on the inside of window trims as they extend onto the bay ceiling, your curtains may not cover the edges of the windows. That would look odd, and very different to the example bay windows. As earlier, if these were my windows I’d definitely be considering 5 roller blinds instead (and probably attaching them to the top of the window frames)