It's normal, though in this day & age of tampon use, some women don't (and boy, in some cultures where virginity is important, can that get them into trouble when bleeding is expected). You're fine, don't be embarrassed. If your boyfriend can't handle the facts of life, find a new boyfriend. lol
It's PERFECTLY normal to bleed down there after sex. Yes it can be embarrassing but it's perfectly normal. How much are you bleeding? Next time you have sex try lubrication so there isn't much friction.