There is a site setting of who can see edit revision pencil in a post. However I don’t believe it is tied to the bumping. But could be wrong.
I adjusted this setting due to some users flagging a post where the author realized their initial post was a bit toxic and edited their post accordingly. Self moderation.
The member who flagged the post even responded:
“I see you edited your post. However I am flagging it, as I can see what you posted originally.”