Newport Gwent Dragons were taught a painful lesson in Belfast at the hands of a merciless Ulster squad which notched up 38 points against the Welsh tally of eight.
Ulster scored five tries with Bowe's brace - he was substituted at half-time in a performance which must have impressed Ireland coach Joe Schmidt - being added to by scores from Ruan Pienaar, Sean Doyle and a penalty try, the latter which brought up the bonus point after only 32 minutes.
Paddy Jackson also put in a notable shift and kicked all five conversion attempts which will also have been noted by Schmidt, who may be without Jonathan Sexton for next week's Six Nations game against Italy.
Ulster led 31-3 at half-time with their only try of the second half coming from Doyle as both sides tired after their five-day turnaround from their previous games.
Ulster opened their account early with a Pienaar penalty after two minutes and then just on the quarter-hour mark Pienaar crossed the line for a try after Ulster countered from their own half.
A Richie Rees high kick was fielded by Jared Payne who beat Matthew Pewtner and then threw a long pass to the advancing Darren Cave who had Pienaar steaming up on his inside to take the scoring pass.
Jackson added the conversion and Ulster were 10-0 up. That became 17-0 eight minutes later when - shortly after Luke Marshall had to leave the field - a Johann Muller lineout off the top saw Bowe hit the line at an angle before racing clear to score.
Jackson converted and did so again three minutes later when Bowe got over again after picking a great line through the Dragons defence which saw Ulster comfortably lead 24-0 after 26 minutes.
The bonus point was racked up just before the half-hour when after a series of five-metre scrums, and with visiting prop Owen Evans in the bin, referee Lloyd Linton awarded the penalty try which Jackson converted taking Ulster's lead to 31-0.
Rhys Jones then hit an upright with a penalty shot for the Dragons but made good with the last action of the half which finished with Ulster leading 31-3.
With Bowe substituted at the interval, Ulster still pushed on with Doyle getting their fifth try five minutes after the restart with Jackson continuing his unblemished record off the tee before he was replaced around the hour mark.
David McIlwaine then had a try ruled out by the TMO for a forward pass from Payne and the Dragons finally got a score from winger Ross Wardle after 63 minutes which Jones failed to convert.
ULSTER: Jared Payne; Tommy Bowe, Darren Cave, Luke Marshall, Rory Scholes; Paddy Jackson, Ruan Pienaar; Callum Black, Rob Herring, Ricky Lutton, Johann Muller (UCD), Iain Henderson, Robbie Diack, Sean Doyle, Roger Wilson.
Replacements: Niall Annett (Herring 72), Tom Court (Black 61), Adam Macklin (67), Lewis Stevenson (Pienaaar 71), Mike McComish (Jackson 62), Paul Marshall (Scholes 54), Stuart McCloskey (L Marshall 20), David McIlwaine (Bowe HT)
Tries: Bowe (2), Pienaar, Doyle, penalty
Cons: Jackson (5)
DRAGONS: Rhys Jones, Matthew Pewtner, Lat Leach, Ashley Smith (capt), Ross Wardle, Steffan Jones, Richie Rees; Owen Evans, Rhys Thomas, Bruce Douglas, Matthew Screech, Cory Hill, Jevon Groves, Nic Cudd, Lewis Evans
Replacements (all used): Nathan Williams, Hugh Gustafson, Duncan Bell, Rob Sidoli, Ieuan Jones, Wayne Evans, Lewis Robling, Jack Dixon.
Pen: R Jones
Att: 12, 960