Center the new window sill in front of the bedroom window opening. On either side, mark where the window sill meets the window opening's sides. Do not include the side jambs in this measurement. Use a level as a straight edge and draw guidelines across the window sill's ends at each mark.
Cut the window sill straight across, following the guidelines, with a circular saw and fine-tooth blade. Test fit the window sill in the window opening.
Apply a bead of construction adhesive along the window sill's length, on the bottom surface. Apply the bead in a zigzag pattern so it covers as much surface as possible.
Slide the new window sill underneath the side jambs on either side of the bedroom window opening and push it as far back as it will go. Secure the sill to the side jambs with screws driven through the bottom of the sill and into the side jambs at an angle.
Run a bead of silicone caulk over the corners where the side jambs touch the window sill's surface. Wipe a finger lightly along the caulk beads to smooth them.