The Gunners' second-in-command was standing in for Arsene Wenger, with the Frenchman serving the first of his three game touchline ban, as goals from Lukas Podolski and Gervinho completed the turnaround after Younes Belhanda had given the home side an eighth minute lead from the penalty spot.
And Bould declared himself pleased with the result, despite facing a Montpellier onslaught in the second half.
He told Sky Sports: "I am really pleased. It was difficult. I thought we were excellent in the first half – we kept the ball and kept the crowd quiet.
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Arsenal have made an excellent start to the season and Bould admitted he was happy to maintain the trend in France, attributing the results to team spirit.
He added: "It's fabulous to get an early away win. We've had a decent start to the season and we have kept the run going so it is important all round, for the whole season.
"We've got great team spirit and I think that was evident tonight. Everybody is digging in and things are looking OK."
Summer signings Podolski and Santi Cazorla were once again prominent in the Gunners' impressive first half showing, and Bould has been particularly pleased with the German's displays.
"Podolski has made a real impact," Bould added. "I have to say, I've not seen many finishers as good as him – ever. Right foot, left foot. He goes in hard in training.
"He's a good trainer, a good boy. He has really added something this year. I'm not getting involved in whether we are missing Robin. Podolski's a good player."
Olivier Giroud started the match on his return to former club Montpellier, and although he failed to find the mark again, he provided a vital assist for Podolski which didn't go unnoticed with Bould.
Bould continued: "Olivier did a really good team job for us tonight. He works really, really hard for the team.
"At set-pieces he is fabulous. He defends and he works for the team. He had one chance at the near post that was difficult. He is a really hard-working boy and I'm sure the goals will come."
And looking ahead to Sunday's Premier League clash with Manchester City, Bould admitted that it will be a tough test against the champions but was confident that Arsenal have what it takes to get something out of the game.
"Of course Sunday is a tough test. We go in there with a bit of confidence, with everybody believing things are going okay," he continued.
"But it is a proper test and that is what we want to do.
"Hopefully we can come through the other side and say we have done okay again on Sunday. Everybody is fine, touch wood. Things are looking quite bright."