This is what I do and dont have any dye coming off when this is finished,
Sand the edge if needed,
dampen the edge,
fiebings edge dye,
then burnish,
fiebings oil dye
then burnish again,
then grab a cloth and rub the edges until they are shining
then beeswax the edge
and burnish
then the beeswax again
and final burnish and polish.
This might seem like a lot of work but you can become pretty quick at this.