Your girl friend can not apply for a B visa so that she can come to the U.S. to marry you. Before you start her permanent residency process, you have to make sure that she is not subject to 2 year foreign residency requirement.
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Using a tourist visa with the intention of marriage is a VERY VERY BAD idea.
You are correct, use a K for her to enter and get married within 90 days of arrival.
Or, you can get married now and she can go home, do her internship, and return with a greencard.
NOTE: You didn't tell us whether or not she has a 2 year restriction on her J. If so, then she needs to stay home for 2 years before coming back as fiance, or spouse.
Franco Capriotti - Senior Immigration Counsel
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IMMIGRATION LAW PROFESSOR for 10 years -- LEGAL DISCLAIMER: This answer is offered for informational purposes only. It does not constitute an attorney-client relationship.