Traditional Chinese girls and their families believe that a future husband should be older, smarter, taller, and better educated than his wife. The acceptable age difference is, generally speaking, two to four years older. As is true throughout Asia, it would be very unusual for a Chinese girl to feel comfortable dating and marrying a younger man. It happens, especially if the age difference is not greater than a year or two, but it is rare.
Chinese girls who deliberately seek much older men generally do so to compensate themselves for having had ambivalent or terribly conflictual, often aggressive, relationships with their fathers. Although this applies to many Chinese girls, perhaps most, it doesn't apply to all. In addition, the preference for older men is typically overrepresented by girls raised by poor families in the countryside and, perhaps, girls who have a history of being cheated on by younger men. The hope is that by choosing a much older man, he is less likely to grow bored with her and chase younger women as time goes by.
As a rule, highly Westernized girls born and raised in international cities such as Beijing, Shanghai, and, to a lesser extent, Guangzhou—especially if their relationships with their fathers were relatively healthy—will not prefer much older men.
At your age of 24, you shouldn't have any difficulty finding recent college graduates, 22- and 23-years of age, who feel it is time to start looking for a boyfriend (read husband). The problem you might run into in second and third tier cities is that most Chinese girls do not believe in monogamous serial dating. That is, most are definitely not looking for just "friends with benefits" or casual sex (see chapter on
Dating Etiquette, Sex, and Relationships in our guide). Having just written that, and especially if you will be teaching in an international city, you will find many girls who are just interested in dating in the Western sense of that word.
If I were 24 years old again and interested in just dating Chinese girls and "acting my age," I'd be limiting my job search to Beijing and Shanghai only--as a way to maximize my chances of finding those type of opportunities.
Best of luck to you.