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A slow song will be easiest for you to sync your movements when dancing. Consider something romantically themed or significant to your partner, like a favorite song. Some DJs accept requests. Requesting a song and asking when that song will be played will help you time your approach. Make full eye contact with you dance partner. Ask her if she would like to dance, but try to make your request in a way that is true to yourself. This will let her know that this is a special moment you want to share with her. You might ask:  May I have the pleasure of this dance? I would be honored if you would do me the pleasure of having this dance. There's no one else I'd rather dance with. Shall we? It's important that you respect her decision, no matter the outcome. Just as it was difficult for you to ask, it will likely be difficult for her to refuse and hurt your feelings. If you notice hesitation, try to be graceful, and never force yourself on your partner. It can alleviate a lot of stress if you come up with a backup plan before making your request. Approach a friend you are comfortable with and explain your situation. If your friend is willing to be your backup, even if you get shot down, you can still have a blast on the dance floor. Be careful not to lead on your friend romantically. Some may have hidden feelings with you, and if this is the case, they may interpret your request as insensitive. Hold out your hand to escort her to the dance floor. Wait until she takes your hand, walking slightly ahead of her to lead her to your spot on the floor.
Choose your moment. Request a dance. Wait for her response. Take the floor.