Most likely your CD burning software is converting the bit rate during the recording process. However, it is probably doing that by simply truncating from 24 bits to 16 - essentially just lopping off the extra 8 bits.
You would be better advised to dither down from 24 to 16 bits. A good dithering algorithm will make the conversion more natural sounding.
As RWhite says, this should be the last thing you do to the file, prior to actually burning to CD.