The 23-year-old returned to practice for the first time earlier today after sustaining the injury in pre-season, but Bradley is still being cautious just days ahead of the start of the season.
He told the club's official website: "He's progressing as planned. It's the next step in his recovery to get back. We're following protocol. It was good. We liked what we saw.
"This is what we expected to see. I think Wednesday will be a big sign to see if he's still in the right direction. Even after today, we'll see how his thumb came out of it."
Jacksonville face the the Kansas City Chiefs in their regular season opener on Sunday.