Defender Marc Bartra fractured his wrist in the incident, which led to Tuesday’s Champions League quarter-final first leg being postponed.
The match has been rescheduled for Wednesday, with a 17:45 BST kick-off.
“In such a crisis situation, all of Borussia will pull together,” said chief executive Hans-Joachim Watzke.
“The team and coaches were shocked. Now we must channel it in some way.”
Watzke said the “explosive strike on the bus” happened as it left the team hotel, with “three explosive devices placed and triggered on the edge of the road”.
Dortmund said Bartra had an operation on Tuesday after “breaking the radial bone in his arm and getting bits of debris lodged in his hand”.
The 26-year-old, who has played 12 times for Spain, joined the Bundesliga club from Barcelona in June last year.
Captain Marcel Schmelzer said: “We’re all in shock and our thoughts are with Marc. We hope that he will make a speedy recovery.”
Goalkeeper Roman Burki, who was sitting at the back of the team bus alongside Bartra, told Swiss newspaper Blick: “We left the hotel and went down the street. The bus turned down the main street, and there was a giant explosion.
“After the bang, we all ducked in the bus and those who could threw themselves to the ground. We did not know had happened.
“We’re all shocked – nobody thought of a football match in this moment.”
The bus was damaged at 18:15 BST on Tuesday – 90 minutes before kick-off – about six miles from the Westfalenstadion in Dortmund.
Police said there were three explosions in the vicinity of the coach and believe the explosives could have been hidden in a nearby hedge.
They called it “a targeted attack” and found a letter at the scene claiming responsibility for the attack, but did not disclose its full contents.
They are preparing for a “large deployment” at the rescheduled game.
Kick-off was initially delayed and, with thousands of fans already inside the stadium, the match was postponed 15 minutes before the scheduled kick-off, with Monaco fans chanting in support of their opponents.
Fifa president Gianni Infantino condemned the incident, while Uefa counterpart Aleksander Ceferin said he was “deeply disturbed” and praised the decision to postpone the game.
Watzke said: “I have to express a huge compliment to our fans, who have dealt with it very well, objectively, reasonably and solidly.
“It will not be easy to get that out of the mind. I think the team will feel it on Wednesday.”
With the second leg in Monaco set for 19 April, Watzke said there was no choice but to play the game on Wednesday, as Monaco have a domestic game against Dijon on Saturday.
Soon after the match was rearranged, people in the Dortmund area offered to host Monaco fans who chose to stay in Germany for an extra night or two, using #bedforawayfans..
And Monaco offered to reimburse their supporters staying in Germany with up to £67 (80 euros).
