Welcome to HCM,
You should avoid intercourse during menstrual periods. You have not mentioned the name of birth control pill you are using. But there are no chances of pregnancy
due to intercourse during menstrual period. Birth control Pills causes withdrawal bleeding only. If you do intercourse during menstrual period, bleeding will be more, but bleeding every time during intercourse in other days is not normal. You should consult Gynaecologist & get yourself examined at your earliest.
Wish you good health,