no. I know why you would want to. It is more comfortable with a bra on to bed. it keeps your boobs in place and if you are sharing a bed you know that your husband/pertner/boyfriend cant fiddle with...
The bra is the wrong size and it sounds like it is too big. Go to a good department store and in the underwear department there is usually a lady who will fit you for a bra that is the correct size.