Apparently the -L flag of samtools that can also do this:

 -L FILE  output alignments overlapping the input BED FILE [null]

So you could do a:

$ ~/bin/samtools view -c results.bam chrI:1-100000
180    
$ cat query.bed 
chrI    0    100000
$ ~/bin/samtools view -c -L query.bed results.bam 
180

bedtools coverage -counts -abam the.bam -b the.gff

Although the PE reads complicate this a little bit, I would say. If this is for counting for genes, I would suggest you look at something like HtSeq-count http://www-huber.embl.de/users/anders/HTSeq/doc/count.html

bedtools AFAIR does not take split reads in the 'abam' file into account.

samtools flagstat

bamtools also has some useful code for this sort of thing under /utils/