You do need to apologize and ask if you can start over. Make your apology to her relatable. We've all had one of those situations where we've gotten ahead of ourselves, nothing seemed to go right, then bad events turned to worse. See if she can understand that experience. Tell her how awful you feel about it happening and how you wish you could have a redo or make it right because she's so special to you. Then, especially if she is still unconvinced, maybe present a written list of the top 10 reasons she should give you a second chance. Hint: make some of the reasons funny, make some of them endearing. Here is a list of song ideas for background mood music:
“We Can Work It Out” by The Beatles (1965)
“Take a Chance on Me” by ABBA (1978)
“You Make My Dreams Come True” by Hall & Oates (1981)
"Smile" by Kracker (2009)
“With a Little Luck” Paul McCartney & Wings (1977)
“I Can’t Fight This Feeling Anymore” by REO Speedwagon (1984)
Although some of these are apology songs, you don't necessarily have to go with that type of song, as many such tunes are about broken romantic relationships and yours hasn't really started yet. Whatever the case, best of luck in winning her over. I hope this was helpful!