The better MBA programs generally want applicants with a strong liberal arts degree rather than an undergraduate business degree. It would be useful, however, to take some basic economics courses (e.g., at least principles of economics 1, 2; and maybe microeconomic theory; macroeconomic theory) as well as courses that develop your analytic and quantitative skills (calculus, statistics, possibly econometrics). If you ended up majoring or minoring in economics, you also might take some courses in corporate finance, international finance, etc. Alternatively, to get some marketable business skills in addition to a liberal arts degree, you could take a principles of economics, some quantitative skills courses, and intro courses in the main business areas: accounting, finance, management, and marketing.
A liberal arts or science degree will not necessarily be a barrier to getting a business job. Liberal arts graduates have writing, analytic, quantitative skills, a "big picture' perspective, flexibility, etc. that businesses value. Many companies prefer to train their own people anyway.
You might also consider some combination of a major/minor in economics and East Asian Studies. You could major in either one of those and minor in the other. This would give you some economics background for business, but also a language and area studies background for pursuing interests in international business, especially involving China. You also could study abroad in China for a summer, semester, or a year. The longer period is better for developing language skills.
I'm not entirely sure where science fits into your plans since you didn't indicate what is the certain field in which you might want to conduct business. For example, if you told me that geology was the science you had i mind, I could well imagine that you had interests in natural resources or energy related business. For other sciences, it's less clear without more specific information. There is no reason, however, why you could not combine a science major or minor with an economics major or minor, or with a core set of business courses.
Another possibility suggests itself, too. You might consider a law degree. A law degree can be very useful in international business. When you learn to think like a lawyer, you may develop valuable analytic, negotiation, and conflict resolution skills that would serve you well in international business. There are parts of Asia, e.g., Vietnam, that still do not have legal systems fully compatible with expected commercial law practices in the rest of the world. Courses in international and comparative law are useful. While that background is the reason that companies hire lawyers, it is a challenging and interesting role to be the lawyer who gets to negotiate and work out the details of a trade or finance agreement. For this type of face-to-face business interaction, cultural understanding is very important as business in many Asian countries (as elsewhere) often depends on personal relationships. There also are areas of law that figure very importantly in business with China and other countries, e.g., intellectual property law. Needless to say, a strong liberal arts background is the best preparation for law school, if that was a path that interested you. At some universities there are joint degree programs in business and law.
As a piece of general advice, I also will mention that if you should find yourself attending a university with a College of Agriculture, don't overlook courses in Agricultural Economics just because you might happen to be majoring in the regular economics dept. in a College of Arts & Sciences. Depending on your specific interests, courses in agricultural and resource economics can be very useful in the areas of international business and finance.
Finally, since one poster mentioned specific schools for you to check out, I'll mention one that has a program I like: Indiana University. Indiana has a special certificate program in Liberal Arts & Management in which you take a series of business-focused seminars in addition to a liberal arts major. The link is here: College of Arts and Sciences 2008-2010 Online Bulletin: Liberal Arts and Management Program
Indiana also will allow students in the College of Arts & Sciences to develop an individualized major, or to do up to 3 minors, including a minor in the business school. Indiana's Kelley School of Business is topnotch. It offers a program in international business and also has study abroad programs, including a couple in China. Indiana has strong programs in East Asian Studies.