The bay can be insulated – I pulled off curved decorative boards in one room, added breathable fibreboard insulation, wopped decorative boards back on and wider windowsill. The rigid insulation was cut into panels about 6″ wide, so creating a neat curve.
What is on the roof of the Bay? is it double height or single storey? If single, again adding insulation boards to a flat roof is not expensive.
Insulate the floor – do you have a carpet? I cannot believe how much warmer one of our rooms is now we have added underlay and carpet. I will be crawling around in the void this winter adding insulation too.
Curtains can be huge helpers – again have curtains that a floor to ceiling, close fitting and lined with thermal insulation. Also more private for when you need to sit naked next to a barely warm mrs_zippy as the room hits 30*.