BEDOPS bedmap is an option, e.g.:

$ bedmap --echo --echo-map reference.bed map.bed > answer.bed

The file answer.bed will contain all elements from reference.bed on each line, with any elements from map.bed that overlap elements from reference.bed.

You can add options to change delimiters or overlap criteria, as well as apply signal or ID mapping operations, etc.

The BEDOPS documentation has more detail:

http://bedops.readthedocs.io/en/latest/content/reference/statistics/bedmap.html

Note: Someone has suggested using bedops --intersect. This answer is not correct, as --intersect calculates new genomic regions where there are overlaps in the genomic intervals in two or more sets, i.e. an intersection.

If you want to map or find associations between two sets, use bedmap to retrieve those associations (or use bedops --element-of, if you do not need to preserve per-element associations, but simply want to see what elements in one set overlap those in another set).