Mapping reads from a BAM file to a custom BED file.

Hi.

I have a BED file that was engendered with the following:

bedtools makewindows -g ../bedtools2/genomes/human.hg19.genome -w 2000 > hg19_2K_bins.bed

The goal is to map reads from a BAM file to the intervals as defined, to visualize the distribution of the counts pan-genome, bin-wise. Now, I am aware of the bamCoverage tool from deeptools, but the incorrigible issue is that it merges adjacent bins if the count number overlaps.

bamCoverage --bam testMe.bam 
            -o testMe_2k.bw 
            --binSize 2000 
            --normalizeUsing None  
            --effectiveGenomeSize 2913022398  # hg19 version of Homo sapiens
            --outFileFormat bedgraph 
            --maxFragmentLength 30

The output I desire is something like:

Chrom Start End Score
chr1 0 2000 34
chr1 2000 4000 46
...

where the values in the last column (Score) are from our BAM file.
I have two questions, basically.

1. Is there an alternative tool for this or a workaround?
2. What if we have a bedgraph/ bw file with scores instead of a BAM?

Please advise. Thanks.