The opening 45 minutes saw neither side able to create any meaningful openings, although Callum Wilson and Marc Pugh did look threatening for the hosts, and Kari Arnason had to throw himself in the way of the former's shot in the 18th minute.
Arnason had the chance to put his side ahead shortly before the break, but his volley flew well wide of the mark.
Wilson should have put the Cherries ahead in the 50th minute after Yann Kermorgant's square ball found his strike partner in front of a gaping goal, but the 22-year-old blazed his shot over the bar.
The young striker came close again a few minutes later, and his shot had beaten Adam Collin, but rebounded back off the post.
The home side's pressure finally paid dividends after an hour when Cook nodded the ball beyond Collin, and Matt Ritchie almost extended the home side's lead, but his low shot was saved.
Rotherham struggled to carve many opportunities, although the introduction of Matt Derbyshire gave them a creative spark and his low cross was inches from finding fellow substitute Alex Revell inside the box with ten minutes remaining.
With that, Rotherham seemed to have spurned their chance to take a share of the spoils, but Bowery headed Paul Taylor's corner into the back of the net to register his first goal for the Millers at a crucial time.