If your goal is make a career of teaching oral English in Asia (specifically China, Thailand, and, perhaps, Taiwan and Korea), then a bachelor's degree in any field with a TEFL certificate more than qualifies you.
If, on the other hand, you would like to have more options, then consider earning a master's degree in linguistics, English, TESOL, or education, seek certification as a teacher in the States, and then limit your search to American-curriculum international schools only: There are several in China, particularly in Beijing, Shanghai, and Guangzhou. As a licensed educator, you could also work at some of the better international schools in Hong Kong and Taiwan as well.
Salaries and conditions at international schools in China are comparable to those you will find in the States and you will be valued and respected as an educator.
Best of luck to you.