http://www.admissions.caltech.edu/content/academic-preparation-requirements says that Caltech requires “4 years of math (including calculus)” for frosh admission, but does not specify BC over AB.
If you are concerned that an admission reader may wonder why you did not take the most advanced math course supposedly available at your school, ask your counselor to note the non-offering of calculus BC in the year you would have taken it.
Caltech Ma 1a (the usual Caltech frosh math course) “will introduce the mathematical method through (One Variable) Calculus. By the mathematical method, what we primarily mean is the ability to express one’s self with absolute precision, and then to use logical proofs to establish that certain precise statements are universally true. We assume that the Caltech freshman has reasonable familiarity with single variable calculus as a computational system, but we emphasize explaining, or testing, why things work and how to justify one’s propositions.” See http://www.math.caltech.edu/~2014-15/1term/ma001a/#des for more information, including lecture notes.