Pre-season favorites City were second best on the South Coast as they went a third game in a row without scoring.
Bournemouth had goals in each half from Brian Stock and James Hayter to thank for their first win of the campaign.
The home side nearly grabbed an early lead in the fourth minute when Steve Fletcher seized upon a poor back pass by Matt Heywood only to see his effort go the wrong side of the post.
An after last season's top scoring Hayter tried his luck from range, Bournemouth took the lead on 20 minutes.
Stock's free-kick from the left edge of the area deceived everyone in the box to find the bottom right-hand corner past the diving Steve Phillips.
City pushed forward in an effort to level matters and Bournemouth defender Neil Young was fortune not to put through his own net when the ball bounced off his knee and inches wide following David Cotterill's cross.
Former Leeds and Sunderland striker Michael Bridges had the best of City's chances and after testing Moss with a 20-yard drive he went even closer seconds before half-time.
Bridges found space in the Bournemouth half and tried a delicate chip over Moss only for the former Southampton man to claw the ball over the bar.
And City's cause was dealt another blow four minutes after the interval when Dave Partridge, making his debut after a summer move from Scottish club Motherwell, handled in the box.
Hayter stepped forward to double his side's lead from the resulting kick.
And Hayter thought he'd added his second of the afternoon moments later only for the offside flag to deny him.
City rallied looking for a consolation goal and Bridges saw a shot go wide before they almost snatched a late goal in controversial circumstances.
With Bournemouth defender Eddie Howe down injured, the visitors continued to play on and Steve Brooker saw his rasping shot from 10 yards well held by Moss.