Context is key. You need to help us help you. Post up pics.

I will wait for the pic. Post it in a comment it is often hard to add to the original

If you POSTED the pic from your phone? You did not wait for it to lose the faded gray look. You must wait for it to appear clear...and then submit /Tap SUBMIT: )

Three inside mount roman shades, or natural woven wood shades.

No curtain panels, no rods, no rings

The molding trim meets the ceiling of the bay, leaving zero room to mount.

Even if they have to be outside mount? A better solution than forcing a square peg in a round hole.

Well it is always helpful to see tthe whole space . The windows now are very formal not really working with a cat tower in my head. Do you need to control heta or UV from the sun ? I often do nothing if those itemsare not an issue . Then if they are my next go to is solar shades they control heat and UV but allow you to keep the view . I use roman shades often on angled bay windows so yes that is a choice too IMO wait until the room is finished then you choose window covering IMO

The room is getting overhauled. I always had a problem with the shape of the window. There is NO room whatsoever for an inside mount for blinds.. less than 3/4" and then the window side locks are in the way. The radius or angle, if you will are not sharp (curved). Its the reason for covering it with the long swag (which I hate). Should I mount one long panel outside where the soffit is? Its pretty far out. Maybe a ceiling mount rod?

Treat each window individually. I think you have room for French return rods.

It looks like you have plenty of room for inside mount, but it might protrude just a bit in front of the trim, which shouldn't be an issue.

If you don't need privacy or light/sun/heat control, why not just leave it uncovered for now and see how you like it?

Yeah, you can see the bay window casing/moulding goes right up to the ceiling/soffit. I also have 2 smaller windows on the next wall where the sofa will go. I'll wait until the room is done before deciding on window treatment. Im still working on furniture set up. Thats in another feed on HomeDiscussions here. The room gets no sun. Just a little when the sun comes up a little mid-day. I want to keep it light and fresh. Blonde wood floors go in next week.

That ceiling is the bay is low to begin with. I would not add any shades that would visually bring the height down. Just fixed panel sheer linen drapes on a rod or cornice board. They will not open or close.