If you have done something really awful to your girlfriend then you may need a big gesture to get out of it. This has to be something really bad, because these are pretty extreme solutions.
Hire a Mariachi Band to Serenade Her
How can a girl resist this? She would be crazy too. If you really want to be crazy then you should serenade her yourself. Make sure you are a good singer though. Be sure to pick a humorous or joyful song; go for a sense of fun, not desperation.
Pay a Someone to Hold Up a Sign for Her
If you live in a major metropolitan area, chances are you and your girlfriend regularly walks by a certain spot, then pay someone to hold up your ,I’m sorry sign. The shock of seeing you publicly declare your sorrow might be enough to get you out of trouble. If you have the money buy her a bill board, but a sign should work well.
Propose Marriage to Her
This one only works if you really want to get married. If you propose to her just to get out of trouble then that is very dumb. It won’t work out and she will be even matter later.
If what you did is not that bad then send her flowers to work and wait for her to cool down. It depends on how bad what you did was if you have to do something crazy or not. She doesn’t have to forgive you, but it is worth a shot.