You are the envy of every person who has ever been pulled over for speeding. Your charm spares you a ticket, and causes the policeman to swoon at your feet. Some gals have all the luck!
Cars in dreams are common metaphors for our selves—for the "direction we are headed" in our lives. Your excess speed shows that things are moving quickly in your life. Judging by the background you provide, we have every reason to suspect it is your romantic life that is in "high gear." As one relationship stalls and loses direction, another appears to be gaining speed. Is it so odd that your dream represents your love life as a drag race, with one car quickly overtaking another?
Police in dreams are common symbols of authority. Accordingly, getting pullled over may reflect your awareness that you need to restrain an "overheated engine." You also may be feeling guilty that you are courting two lovers at the same time. The conclusion of your dream, however, reveals your true feelings. You don't believe you are guilty of committing a crime (the policeman doesn't write you a ticket), and you are confident that you will reach your hoped for destination: a passionate romance!
The policeman in your dream is a literal allusion to the law enforcement profession—of which both your suitors are members. Because your new suitor recently confessed his feelings for you (you are his dream woman) it appears this dream of "love in the fast lane" already has come true. Congratulations on your new romance.