Bournemouth were a little flattered by the margin of their win with Bury every bit as creative in an equal first half, but the Lancashire side fell away after the break and conceded three late goals.
Brett Pitman put Bournemouth ahead in the eighth minute with his third goal in successive matches, but Bury deserved to be level and after Bournemouth defender Dan Seaborne had lost possession, Craig Jones crossed for Andy Bishop to head a 24th-minute equalizer.
Bournemouth took complete control in the second half 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 and substitute Matt Tubbs added a fourth from close range in the 89th minute.
Blackwell, who could name only four substitutes on the bench due to injuries, said: "This is the toughest season I have known. 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."