1. May I invite you to dance with me?
您能赏光跟我跳个舞吗？
还能这样说：
How about a dance with me?
Can I have the honor to dance with you?
应用解析：
be invited out 应邀，被邀请；
invite oneself 不请自到；
invite sb. along 邀某人做伴；
invite sb. up 请某人上楼
2. May I have the honor of asking you for the first waltz?
能有幸请您跳第一曲华尔兹吗？
还能这样说：
May I have the pleasure of the first waltz?
May I have the first waltz?
谚语：
There is honor among thieves.
盗亦有道。
3. We danced to the music.
我们和着音乐跳舞。
还能这样说：
We danced to the accompaniment of music.
We danced with the music.
应用解析：
dance for joy 快乐得手舞足蹈；
a song and dance 众说纷纭；小题大做；
give a dance 举行舞会；
dance to another tune 改变主意或态度
4. Their dance steps are graceful and the music is also pleasant.
他们舞姿优美，音乐也很不错。
还能这样说：
The music is wonderful and they also dance beautifully.
These dancers are graceful and the music is splendid.
谚语：
Every lover sees a thousand graces in the beloved object.
情人眼里出西施。