It's a bit unusual to have genes in bed format, but I suppose that could be used. If you had the genes in GTF or GFF format, the normal reply would be to simply use htseq-count, but that won't work with your bed file. Your best bet is to load the bed file into R and create a GRangesList from it. Then you can open your SAM/BAM files and use countOverlaps to get per-gene counts. I suspect that creating a properly formatted GRangesList from a BED file will prove non-trivial, but it should be doable.