As with most interval operations, bedtools has a command for it:

https://bedtools.readthedocs.io/en/latest/content/tools/flank.html

 awk -F '\t' '{X=10000; B=int($2);E=int($3);printf("%s\t%d\t%d\n%s\t%d\t%d\n",$1,B-X<0?0:B-X,B,$1,E,E+X);}'

If you are using R, you can do it with the flank function in GenomicRanges. It takes into account the chromosome lengths, if present.

https://bioconductor.org/packages/3.7/bioc/vignettes/GenomicRanges/inst/doc/GenomicRangesIntroduction.pdf

Yep, just use BEDOPS bedmap --range to map padded elements:

$ bedmap --skip-unmapped --echo-map --range 10000 reference.map map.bed | awk '(!a[$0]++)' | sort-bed - > answer.bed

We use awk to strip duplicates from unsorted results. Sorting is necessary because we use --echo-map, where mapped elements can be returned out of order.

The file answer.bed will contain unique elements from map.bed that overlap elements from a 10kb-padded version of reference.bed.

Here's another approach that uses bedops --range:

$ bedops --merge reference.bed | bedops --range 10000 - | bedops --element-of 1 map.bed - > answer.bed

The file answer.bed will contain unique elements from map.bed that overlap elements from a 10kb-padded version of reference.bed. Adjust padding, as needed.

Merging the reference intervals before padding should handle overlaps, which avoids the need to filter duplicates and resort. So this should work faster than using bedmap --range, I think.