When communicating with your boss, it's important to be polite and professional. Here's an example of how you can inform your American boss that you already have plans for the evening and won't be able to attend the dinner with the company:

Dear [Boss's Name],

Thank you so much for inviting me to the dinner with the company. I really appreciate the gesture and the opportunity to spend time with everyone outside of work. However, I regret to inform you that I already have plans scheduled for that evening.

I apologize for any inconvenience caused by my prior commitment. If there's an alternative date or event in the future, please let me know, and I would be more than happy to participate and contribute to team bonding activities.

Once again, thank you for including me, and I hope the dinner is enjoyable for everyone. Please feel free to reach out if you have any further questions or need assistance with anything else.

Best regards,
[Your Name]