The bedtools makewindows command can do this (and other useful "stuff") as well:

bedtools makewindows -b test.bed -w 1
chr1    10    11
chr1    11    12
chr1    12    13
chr2    100    101
chr2    101    102
chr2    102    103

That said, you can't deny general utility of the nice awk approach that Alex describes - easy to adjust...

Not with BEDOPS, but you can run your BED file through awk:

$ awk ' \
    { \
         regionChromosome = $1; \
         regionStart = $2; \
         regionStop = $3; \
         for (baseStart = regionStart; baseStart < regionStop; baseStart++) { \
             baseStop = baseStart + 1; \
             print regionChromosome"\t"baseStart"\t"baseStop; \
         } \
    }' regions.bed > bases.bed