As I read the translations of your questions, I am not completely sure you are trying to open an Illustrator file "with" Bridge or "from" Bridge. I am going to assume that you are seeing an Illustrator file in the Content Panel of Bridge and trying to open that file.
First off, please be sure that you have updated Bridge and Illustrator to their latest releases.
Second, go into Bridge's Preferences and then select the File Type Associations as shown below. Make sure that you've got Adobe Illustrator selected to open the .ai suffix.