The Cherries were knocked out of the FA Cup by non-league Blyth Spartans on Tuesday but they bounced back to beat a Bury side with the best away record in League Two this season.
Sammy Igoe opened the scoring in the 39th minute when he clipped home after being teed up by striker Matt Tubbs.
Welsh Under-19 captain Partington sealed the victory six minutes later, with Tubbs providing another assist.
Bury were disappointing throughout although top scorer Andy Bishop missed a glorious chance to get them back in the game four minutes from time.
Bournemouth striker Alan Connell almost grabbed a third for the hosts in injury time when he ran clean through but his shot was well saved by goalkeeper Wayne Brown.