The Oscar-nominated actor is in the area shooting his new film American Hustle. Bradley (left) was joined at the bedside by American Football star Julian Edelman (right) of the New England Patriots, a celebrated local team.
Julian tweeted a photo of their visit to Boston Medical Center, describing the 27-year-old patient as a "stud" and "a true inspiration".
The young American has been hailed as a hero after giving police a description of one terror suspect, while still groggy from his operation.
His brother Chris told Bloomberg TV that Jeff saw a man with a hooded sweatshirt look at him and then drop a package at the finish line.
"He woke up under so much drugs, asked for a paper and pen and wrote, 'bag, saw the guy, looked right at me,'" said his brother Chris.
FBI officers used the description while surveying video footage. Jeff had been cheering on his girlfriend Erin Hurley, who was running the race.
Friends and family have set up a facebook page to support him on the long road to recovery. His colleagues at a local store also found a novel way to boost his spirits, sending him a photo of themselves lying on the ground to spell out his name.
Meanwhile, his best friend posted: "Baumans doing awesome, another successful surgery and he's talking, making jokes and in very good spirits, I told him about the outpouring of support and the candlelight tonight he couldn't believe it says 'Love you guys.'"
Victims of the senseless tragedy have also received the personal support of President Barack Obama.
Speaking at an inter-faith service in the city, he told "the people of Boston and the families who've lost a piece of (their) heart", "a bomb can't beat us". "We carry on. We race. We strive. We build, and we work, and we love."
The US leader also said that all Americans have "been touched by this attack on your beloved city. Every one of us stands with you."
He concluded by predicting that this time next year "the world will return to this great American city to run harder than ever, and to cheer even louder, for the 118th Boston Marathon".