The in-form Cherries were stunned when Jeff Hughes headed freefalling County into a second-minute lead from Joss Labadie's cross.
But Eddie Howe's side gradually gained the upper hand with Simon Francis, Brett Pitman and Eunan O'Kane all going close.
It was only a matter of time before Bournemouth levelled and Ritchie did so in style with a vicious low 17th-minute shot after Charlie Daniels and Marc Pugh had sliced County open down the left.
Brett Pitman doubled Bournemouth's lead midway through the first half with a low 25th-minute shot, his sixth goal in as many games.
County's problems increased on the stroke of half-time when midfielder Andre Boucaud was sent off for a second bookable offence.
Bournemouth's Ryan Allsop made a fine finger-tip save to deny Labadie after the break, while Harry Arter was similarly foiled by Bartosz Bialkowski.
Ritchie wrapped up the points for Bournemouth with a third goal five minutes from time after substitute Lewis Grabban had worked the ball in from the right by-line.