I agree that it looks like ivory linen. Check Pottery Barn or Restoration Hardware for ivory linen drapes. RH is more expensive, but they are gorgeous. I have four ivory RH panels in my bedroom.

I actually like the paint colour. I think your curtains are too long, and they look like they're sagging. I would move the rods up to make them look less like a girl with too long hair. And put a longer rod on the one on the right so it hangs beside the rad, not twisted to the side. I also think the wall arrangement needs more life. Either bigger frames, more pieces, more colourful art or matts, or just space it out more.

If you indeed like color and pattern, go for it! Everything goes with black and white. Please don't be boring and get white towels and rug. How about a stripe for the towels? Or a contrast band on a solid color? Maybe an ombre effect rug. I do use light colors mostly in my own bath, light blue and sandy color, not for ease of washing, but because they go with my shower and floor. You can get any color perfectly clean without bleach by using an oxygen cleaner or vinegar in the wash. Less harsh on the fibers.

Do you need any daytime privacy? If you want them off the windows completely they would be outside mount on the wall and I would hang them from below the moulding to the floor but not at all dragging on the floor. You could put a very flat panel of semi sheer material just against the bottom sash for privacy, which would allow light and view above, and then a full panel to each side from cornice to floor. I don't know that I would do one on each side if they are just for aesthetics. I picked a color from the rug just so you could see them, it's not a color suggestion. I would probably do a pattern that was mostly wall color with some of the other colors of the carpet, if you could find it.