We present a constant round protocol for Oblivious Transfer in Maurer's bounded storage model. In this model, a long random string R. is initially transmitted and each of the parties interacts based on a small portion of R. Even though the portions stored by the honest parties are small, security is guaranteed against any malicious party that remembers almost all of the string R. Previous constructions for Oblivious Transfer in the bounded storage model required polynomially many rounds of interaction. Our protocol has only 5 messages. We also improve other parameters, such as the number of bits transferred and the probability of immaturely aborting the protocol due to failure. Our techniques utilize explicit constructions from the theory of derandomization. In particular, we use constructions of almost t-wise independent permutations, randomness extractors and averaging samplers.