But the talk about Ellsbury won't go away any time soon, at least when reporters remind Bradley of the proverbial shoes he is trying to fill.
"I don't have shoes to fill," said Bradley, who is ranked Boston's No. 3 prospect. "I'm just trying to fill my own shoes -- size 10 and a half. Just trying to do what I can do."
If it isn't Ellsbury that Bradley is being asked about, it is Grady Sizemore, who is on the comeback trail with the Red Sox.
Everywhere there are reminders of star center fielders -- the type of player Bradley hopes he can be.
And yet Bradley remains remarkably unflappable about the whole thing. There is no look of panic or worry anywhere around him.
"We don't do the talking," Bradley said. "We just do the playing. If it makes for a good story, that's great. We're just going out there playing and trying to prepare for a season. I don't really get too caught up in it. Just go out there and play the game."
That's what Bradley did on Tuesday against the Yankees on a day Ellsbury was idled by an injury and Sizemore was resting in Fort Myers.
Starting in the leadoff spot, Bradley was 1-for-4 with a laser double to right-center in the third.
"Good swing on the double into right-center field," said manager John Farrell. "I thought his first at-bat against [Michael] Pineda was another quality at-bat where he was aggressive at the plate. Borderline strike three in the final at-bat."
Yes, the pitch Bradley was rung up on in the seventh was perhaps shoulder high. And for one of the few times you will ever see, Bradley showed some emotion, giving home-plate umpire Greg Gibson a double take.
But Bradley was over it, showing no signs of frustration when he reached the clubhouse a few minutes later.
"That's baseball. Move on, get over it," said Bradley. "I felt it wasn't a strike. On to the next."
While Sizemore is hitting .381 , Bradley is at .189. But Grapefruit League batting average will have next to nothing to do with the ultimate decision made by Farrell and Boston's front office.
"What we're focusing on is not a batting average, but the quality of at-bats," Farrell said of Bradley. "They're getting more consistent."
Bradley's demeanor these days is no different than last year's Spring Training, when he was the best hitter in camp, finishing the Grapefruit League with a .419 average.
Roughly a month shy of his 24th birthday, Bradley's even demeanor should position him for success in a sport in which the best players make outs in seven out of every 10 at-bats.
"Yeah, he's a mature guy," said Farrell. "He knows who he is, and I think that's a sign of maturity."
This is no small thing in a sport where the mental aspect of the game can defeat prospects trying too hard to live up to the hype.
"He's pretty secure in who he is as a person and a player," Farrell said. "He's come into this camp not trying to show that he's a replacement to Jacoby. He's going out to be the best player he can be and that might be a different skillset. As we've expressed to Jackie, we're looking to put together a team that's going to be a top five scoring team in the league, and we may do it a little bit differently because of the personnel here, but we're not looking to replace Jacoby Ellsbury."
The one thing that figures to be as consistent as Bradley's demeanor is his defense, where he has always excelled.
He made a tough catch look easy against the Yankees, gliding back to the wall to flag in a shot by Alfonso Soriano.
"I got a good read off of it," said Bradley. "I looked up and I was trying to stay away from the sun. The sun was off to my left. I actually lost it for a second, but I was able to pick it back up at the last minute."
And if it isn't until the last minute of camp that Bradley learns his fate for the start of the season, you can be fairly certain he's not going to lose a minute of sleep fretting about it.
"I don't worry about it. I just be me," Bradley said. "Nothing's given. I'm at peace with everything. I can't control it. I don't try to."
It was also pointed out to him that the player can't always control when the opportunity comes.
"That's right," Bradley said. "You don't. Be ready when it does."