Brett Pitman put Bournemouth ahead in the eighth minute. However, Bury deserved to be level and Craig Jones crossed for Andy Bishop to head a 24th-minute equaliser. Bournemouth took complete control from the moment Ritchie blasted home from 25 yards in the 55th minute.
Bury struggled to contain Bournemouth after that and did well to hold out until the 80th minute when midfielder Harry Arter blasted in an unstoppable volley. Substitute Matt Tubbs added a fourth from close range after good work by Eunan O'Kane in the 89th minute but it was Ritchie who caught Howe's eye.
Howe said: "This is the first time we have been able to play Matt in his best position on the wing and he showed just what a good player he is. We have had to play him at left-back and he did extremely well, but his natural position is on the wing because he is goalscorer and a goal-creator.
"We scored some great goals. We were the league's leading scorers for a time before a dry patch, but we are showing signs of recovering in that respect. The league is very tight and we are aware that we need to win by bigger margins. Goal difference could be vital at the end of the season.
"We lost a few important players to injury, but we have got most of them back now and that is bound to help."
Bury boss Kevin Blackwell lamented the loss of players to injury, which left him with only four substitutes on the bench.
"This is the toughest season I have known," he said. "The football club has been on the back foot for a long time on and off the pitch. We only had four subs and picked up two more injuries, but the lads keep going. Even though we lost 4-1 against a very good Bournemouth side, it did not reflect on the way we played.
"Andy Bishop was a real handful in the first half and only a top-class save by their goalkeeper stopped us going in at half-time 2-1 up. But in the second half Bournemouth were too strong for us and scored some great goals.
"We are still in with a chance of staying up. When I came here in October we were 14 points adrift. We have seven matches left and I believe we can get enough points from them to stay up."