You are really unfair to him, singling him out while at least 2 other players have done worse than him particularly on this first goal. Actually the way I see it, regarding his positioning Bellerin was spot on in his movement for their first goal.
This is where it starts. Bellerin is right were he is supposed to be, minding their left attacking player (Fraser), Daniels is way behind and Ramsey is doing fuck all.
Here you can see Fraser starting to make a run behind Mustafi's back (you can see him pointing with his hand that he wants the ball behind Mustafi). Bellerin again is exactly where he is supposed to be, minding their left attacking player and covering his run, Mustafi is actually the one who is drawn too much to the left and is completely unaware of the run behind his back. Bellerin has no choice but to cover that run and it is no business of his to mind their left back at this point. Look at Ramsey, absolutely no action in the center of the park and there are two players behind his back, invading his zone (right midfield). If Bellerin stays to the right (which he shouldn't) there's a huge gap in the center of the defense.
This is the moment where it is already too late for us. Daniels has invaded our field through the right flank of our defense while Ramsey has done fuck all defending (defending is not only done where the ball is), maybe thinking he is a center midfielder. Daniels is waving his hands for the ball, rubbing his eyes at all the space Ramsey has left for him down the right flank.
Right after this moment there is an episode where Ramsey turns his head to check the space behind him. A few moments later the long ball towards Daniels is played and Ramsey points to Bellerin to cover the space instead of doing just that himself. What sort of right midfielder does that? Maybe one who doesn't think of himself as one, unaware of his role on the pitch.
This is the moment he points.
This is the moment of the pass.
Ramsey, who knows their left back is all alone down our right flank, instead of covering that area is moving inside. Bellerin is not too far inside, his movement is defined by the movement of the center half. If he starts covering the area behind him too early (before the pass is played), he leaves the center of defense completely exposed. At this point if Mustafi moved to the right, Bellerin would have moved to the right but since Mustafi is still inside the left side of the pitch, Bellerin covers centrally. You can see Stanislas I think who is next to Xhaka also getting ready to make a run so imagine all the space in the center of defense if Bellerin moves to cover for Daniels before the pass is played.
All in all this is a collective defensive error (including midfield defending) and also credit to Bournemouth for exploiting the spaces between our defenders well but in no way is Bellerin at fault for this goal imo. I think there is little shame if you get turned by the attacker when defending at speed and it's premature to call it his fault only because the goal happened in the area of the right back.