The 26-year-old Spain international had surgery on his right hand and wrist following the blast, which happened ahead of a Champions League quarter-final tie against Monaco on 11 April.
He completed a first training session back with his team-mates on Wednesday.
"I've been looking forward to this moment for weeks," Bartra tweeted.
Three devices containing pieces of metal exploded shortly after Dortmund left their hotel to travel to the home leg of their last-eight tie against Monaco.
Police in Germany have charged a man suspected of being behind the attack. Prosecutors say he was a market trader hoping to make money if the price of shares in the team fell.
Bartra, who joined Dortmund from Spanish champions Barcelona last June, was the only player to receive serious injuries in the blast.
He wore a cast on his right arm and posed for a selfie with his team-mates as he made his training-ground return.
Dortmund, who are third in the Bundesliga table, have two more league games to play this season, while they meet Eintracht Frankfurt in the German Cup final on 27 May.
Borussia Dortmund defender Marc Bartra has returned to full training, a month after being injured in a bomb attack on the German club's team bus.