You truly do only have a single opportunity to make a first impression. If you've had this opportunity and things didn't go quite as expected, you may have inadvertently made the other person leery of spending time with you. Fortunately, a heartfelt apology can make your first impression have less impact than it initially did. Being honest in apologizing for your faux pas can go a long way in letting the other person know you are willing to accept responsibility for your mistakes. This, second, impression can outweigh your less-than-stellar first impression.
Apologize, just once, but make sure it's meaningful. When you've made a bad first impression, your first inclination may be to shower the offended individual with multiple apologies. This may seem a good approach to distract her from your bad first impression, but it usually causes additional damage to your already tarnished image. Provide the person in question with a single statement of apology that clearly defines what you said or did and expresses that you are sorry. Avoid inferring how the person is feeling and instead use "I" statements, which keeps the onus on you.
Interject a bit of self-deprecating humor into your apology. If you can't laugh at yourself, you're taking things too seriously and might not be prepared to hear the other individual response to your apology. Step back and consider the humor in what you said or did that led to the bad first impression. Use the lighter side of what happened as you explain, for instance, "I found out that when I'm in your presence, I lose the ability to make simple sentences." When you're being humbled by your behavior, smile, at the least, or laugh a little in order to show your very human side.
Suggest a second chance at a first impression. You can't take back what you've already done, but you certainly can request a "do over." If you made a bad impression in the course of your first date with a woman, ask her if she'd like to go out on an informal, no-pressure second date. Avoid making extravagant plans and instead suggest circumstances that are similar to those of the first date. Consider this as a second shot to do the right thing, although it isn't actually a first impression. At the very least, you may experience less anxiety about the prospect of a date with her, since you already have an idea of how it might progress.
Determine a reasonable token of your appreciation that can also act as a way of saying "I'm sorry." A bouquet of flowers or a card can serve as a tangible gesture of wanting to make things right again. Giving something with your verbal apology also provides a reminder of your commitment to not make the same mistake if given a second chance. Avoid going overboard with a token of appreciation. Giving a nice watch, for example, probably isn't appropriate for your second opportunity to make an impression.