Bowerman hooked home from six yards after 89 minutes to secure Walsall a third away win and increase the pressure on Cherries' boss Paul Groves, whose side are still chasing their first home win of the season.
James, who signed a season-long contract on Thursday, was earlier left helpless when Bowerman's cross found
Andy Butler unmarked eight yards out and the Saddlers' skipper headed Walsall into the lead.
Walsall were good value for their win and Bowerman had twice gone close before they took the lead, first planting a header wide and then clipping a first-time effort inches past the post.
It took Bournemouth 47 minutes to muster their first shot on target with Eunan O'Kane's low effort scrambled around the post by Saddlers goalkeeper Karl Darlow.
Bournemouth thought they had earned a late point in the 81st minute when Charlie Daniels latched on to a loose ball to drive the equaliser past Darlow, but the point was snatched away by Bowerman's late winner, which prompted the home crowd to call for Groves' head.