I will guess that bride price means dowry. In many cultures, a bride's family will pay money to the groom's family. It isn't common at all in western culture, but the practice exists in some cultures and religions today.
I think bride price and dowry are different. Bride price is money or property or wealth "paid" to the parents of a woman for the right to marry their daughter. A dowry is paid to the parents of the groom or to the groom himself.