Graham Turner spent 15 years at Hereford as owner, chairman and manager before leaving for Shrewsbury in 2010 and Bowman's double made sure his first trip back ended on a losing note.
The Bulls got off to a dream start when Will Evans poked home Chris Todd's knock down but had a lucky escape four minutes later when Marvin Morgan hit the post for the Shrews.
Bowman unleashed a 25-yard drive to make it 2-0 in the 12th minute before Luke Summerfield pulled one back for Shrewsbury with a delightful curling free-kick.
But that was all the Shrews could manage with Bowman wrapping up the win for Hereford from the spot after being tripped himself by Lee Collins with 17 minutes left.
