Alexis Sanchez's omission from the matchday squad had sparked rumours of an impending move to Manchester United and Arsene Wenger admitted as much in his pre-match press conference as the Chilean winger inched toward the end of a six-month-long saga.
Arsenal return to action on Saturday with a Premier League home clash against Crystal Palace.
Mesut Ozil was also missing because of injury and Arsenal's lineup looked a shadow of the past teams under Wenger.
Alexandre Lacazette, a player who has been low on confidence of late started up top - and with Sanchez departing the Frenchman now has an even bigger onus on him to become Arsenal's main goal scorer, something he couldn't manage on the day.
Danny Welbeck, Shkodran Mustafi and Maitland Niles all came close to breaking the deadlock in the first half but Bournemouth remained compact at the back. Iwobi slotted an excellent pass inside left-back Charlie Daniels, allowing Bellerin to advance on Begovic before beating the keeper with a powerful angled shot.
But in a tightly contested first half neither side were able to get a shot on goal as it remained goalless at the break.