The correlation function in R is called cor(). The help page for it is accessed with "?cor" and it will tell you how to easily compute Spearman and Pearson by using the "method=" parameter.

Before any of that can make sense, you need to realize that correlation is a function of sets of numbers, not 'bed files'

If you meant to compute correlations of a particular column of the BED, after perhaps merging the two on genomic coordinates, that's another question entirely. try "bedtools".