Depends on the BED data you want to convert to GTF. If your raw data was originally a GTF file converted with BEDOPS gtf2bed, then the lossless conversion result (BED-formatted) contains all the columns you need to rebuild the original data, by simply printing out columns in a different order and setting the correct coordinate index:
Changing the coordinate is really simple, just add one to the start coordinate. But the GTF format also needs attributes such as gene_id and transcript_id fields that are not present in the BED format. Therefore you will need a third source of information.