But you example output does not seems correct:

scaffold11296 36365 36414 overlaps with two + regions from file B.

scaffold11296   36339   36370   +
scaffold11296   36340   36369   +

One way, via bedmap and bedops:

$ awk '$4=="+"' B.bed | bedmap --echo --count --delim '\t' A.bed - > count.for.bed

Another way, via a bash script that just uses bedops:

#!/bin/sh

referenceFn=A.bed
mapFn=B.bed
answerFn=count.for.bed

while read line
do
    echo -e ${line} \
        | bedops --element-of 1 ${mapFn} - \
        | awk -vline=${line} ' \
            BEGIN { plus = 0; } \
            { if ($4=="+") { plus++; } } \
            END { print line"\t"plus; }' - \
        > ${answerFn}
done < ${referenceFn}

The first approach via bedmap will likely run somewhat faster. It is also (to my eyes) a lot more readable.

On the other hand, the second approach that works on each line of the reference file (A.bed) gives you more control. With this approach, for instance, you could count overlaps of both forward- and reverse-stranded elements in one pass (as noted in the answer to your forum post):

#!/bin/sh

referenceFn=A.bed
mapFn=B.bed
answerFn=count.both.bed

while read line
do
    echo -e ${line} \
        | bedops --element-of 1 ${mapFn} - \
        | awk -vline=${line} ' \
            BEGIN { plus = 0; minus = 0; } \
            { if ($4=="+") { plus++; } else { minus++; } } \
            END { print line"\t"plus"\t"minus; }' - \
        > ${answerFn}
done < ${referenceFn}

Yet another UNIX-based way to do this would be:

$ awk '$4=="+"' B.bed | bedmap --count A.bed - > count.for.txt
$ awk '$4=="-"' B.bed | bedmap --count A.bed - > count.rev.txt
$ paste A.bed count.for.txt count.rev.txt > count.both.bed