BEDOPS bedops --range L:R with bedmap and gff2bed may be another option. The order of the two input files in bedmap specifies whether they are reference or map, respectively.

First, use awk to separate inputs by strand:

$ awk '($6=="+")' input.bed > input.for.bed 
$ awk '($6=="-")' input.bed > input.rev.bed 
$ gff2bed < input.gff3 > input.gff3.bed
$ awk '($6=="+")' input.gff3.bed > input.gff3.for.bed 
$ awk '($6=="-")' input.gff3.bed > input.gff3.rev.bed

Then map the GFF annotations to asymmetrically-padded regions, leaving out any GFF annotations that do not overlap padded reference elements:

$ bedops --range -50:500 --everything input.for.bed | bedmap --echo-map --skip-unmapped - input.gff3.for.bed | sort-bed - > answer.for.bed
$ bedops --range -500:50 --everything input.rev.bed | bedmap --echo-map --skip-unmapped - input.gff3.rev.bed | sort-bed - > answer.rev.bed

Then take the union the two stranded results:

$ bedops --everything answer.for.bed answer.rev.bed > answer.bed

Hope this helps!