just write as usual, see mine inside

Dear mom, her name in PinYin (Chinese names here in bracket),

I'd like to invite you to visit me in San Francisco, California, USA. United States is a great country with many beautiful parks, historical architecture, and diverse cultures. The American people are very open-minded, innovative, and courageous. We can visit these places together with your US-born grandson. I will be responsible for all your expenses including air fare, health insurance, food, and shelter. Please take your passport and this letter to US embassy in Beijing to get visiting visa at your earliest convenience. We all look forward to seeing you soon in USA.

Sincerely,

Your daughter, my Enlish name (my chinese characters in bracket).