No experience with this, but you probably want GenomicRanges package and its functions such as findOverlaps and nearest. Essentially the same as bedtools just in R. If you want to map regions to genes in a certain window then simply extend either of them using GenomicRanges::resize and then use any of the overlap function from that package, e.g. findOverlaps, subsetbyOverlaps etc to get the overlaps. nearest in case you want the closest gene/region. Be sure that you use the strand options since it is the gene start coordinate that matters and if a gene is on the minus strand then the actual end coordinate is the start.