If you can use BEDOPS tools, you can use pipes and process substitutions pretty easily.

For instance:

$ bedops --intersect <(closest-features --closest A.bed query.bed) B.bed > answer.bed

Or:

$ closest-features --closest <(bedops --intersect A.bed B.bed) query.bed > answer.bed

Or:

$ closest-features --closest A.bed query.bed | bedops --intersect - B.bed > answer.bed

Or:

$ bedops --intersect A.bed B.bed | closest-features --closest - query.bed > answer.bed

Etc.

It just depends on what you're trying to do. Your question might be a little unclear, in that an intersection operation on two sets A and B will calculate elements which are always zero units away from B. Feel free to clarify what you're trying to do, if that's not the case.