One way, via bedops and vcf2bed:

$ bedops -e 1 <(sort-bed regions.bed) <(vcf2bed < variants.vcf) > answer.bed

If you want the associations between regions and SNPs, you could use bedmap:

$ bedmap --echo --echo-map --skip-unmapped --delim '\t' <(sort-bed regions.bed) <(vcf2bed < variants.vcf) > answer.bed

This prints each region and those variants which overlap a region. If a region does not contain any variants, --skip-unmapped skips over that region.

Reference:

• https://bedops.readthedocs.io/en/latest/content/reference/set-operations/bedops.html#element-of-e-element-of
• https://bedops.readthedocs.io/en/latest/content/reference/file-management/conversion/vcf2bed.html
• https://bedops.readthedocs.io/en/latest/content/reference/statistics/bedmap.html#echo