So, more of a bow window than a bay window, per the usual terminology where the smooth curve is a bow.
The typical approach is to kerf the back of the piece you need to bend. Depending on the profile, this can be simple or more difficult - the basic concept is to make a cut every 1/2 inch or centimeter (approximately - don't get fussy about measuring them!) that leaves only 1/8-1/4" of wood on the face intact, at which point the board should bend into place easily. If there is a molded profile on the face of the board, this becomes trickier, since you need to be careful not to cut through the board where the molded profile is deep.