You can break your hymen by riding a bike, or riding a horse, or any number of things. Blood doesn't necessarily mean a broken hymen however. When your hymen
does break, it generally hurts quite a bit, but not always. Your boyfriend may have broken it with his finger, or it may have already been broken, or maybe he was too rough and accidentally cut your vagina with his nails, or just by force if he doesn't have nails long enough to do that. Assuming you broke it and didn't realize it, he may have hit your cervix, as that does happen sometimes during intercourse and can cause vaginal bleeding.
Also, i'm not sure why your mother would be ask a doctor to see if your hymen was still intact, or if she doesn't ask him, why he would volunteer that information. It's not a big deal to have a broken hymen, and doesn't mean you've had intercourse. And assuming you are a virgin, there is really no need for you to have a pap smear or any other examination where a doctor would be looking inside of your vagina.
It also doesn't mean you aren't a virgin. I broke mine riding a bike when I was 8 years old, and obviously remained a virgin for a number of years after that.