To see bites in your dream is an indication that someone you trust may try to cause you pain. They may try to injure you or cause you financial losses. Don't be too trusting and naive.
To dream that you are being bitten symbolizes a situation that has been frustrating you. You feel helpless to overcome this hurdle and are unsure of which tactic to take.
To dream that you are being bitten by a vampire implies that someone has been taking advantage of you. You must see this person for who they really are and stop allowing them to influence you negatively.
To dream of biting someone indicates that you are being too controlling or you are being too hard on someone. It's possible that you are jealous or mistrusting. You need to acknowledge these feelings and understand why they exist. Stop being so dominating and ease up on your behavior.