"The pain, the panic, the uncertainty of not knowing what was happening, or how long it would last... they were the longest and hardest 15 minutes of my life," the Spanish defender wrote in a message posted on Instagram.
The bombs containing metal pieces detonated minutes after the team bus set off to a Champions League game against Monaco on Tuesday night.
Bartra was hurt by flying glass and had to undergo wrist operation, taking him out of action for four weeks.
The 26-year-old said "the shock of the past few days is diminishing all the time" and that when he looks at his swollen wrist, what he feels is "pride".
"I look at it proud thinking of all the damage they wanted to do to us on Tuesday and it resulted in just that," he said, thanking those who are treating him as well as fans, his team-mates and others who have showered him with support.
"I needed to write and get this off my chest and settle it so I can just think about getting back to 100 percent as soon as possible," he added.
'Most Germans feel safe'
Three days after the attack that injured Bartra and a policeman who suffered trauma from the noise of the blasts, investigators are still scrambling to find possible culprits.
The probe suffered a setback on Thursday when the sole suspect in custody was cleared of involvement in the crime.
Investigators had zeroed in on two suspects believed to belong to a large jihadist scene in western Germany's Ruhr region, after three identical letters were found at the site of the attack.
The letter demanded that Berlin stop its Tornado reconnaissance missions in the international anti-IS coalition and close the US air base at Ramstein, western Germany.
But the head of domestic intelligence for the region, Burkhard Freyer, said investigators had not ruled out the extreme-right, the far-left or hooligans of being behind the attack.
Germany has been on high alert since a series of jihadist attacks last year, including a deadly Christmas market truck rampage in Berlin.
Despite the attack, most Germans still feel safe, according to a poll of 1,000 people a day after the blasts by public broadcaster ARD.
Some 82 percent polled said they "feel rather safe", said ARD. Likewise, a majority - 56 percent - of those surveyed said they felt well protected against terror attacks.
Dortmund, who eventually played the delayed match against Monaco a day after the attack, are preparing to host Eintracht Frankfurt in the Bundesliga on Saturday.
The club's manager Thomas Tuchel had hit out at the decision to play the Monaco Champions League game so soon after the assault, saying they were treated as if only a "beer can" had been thrown at their bus.