Ospreys captain Dewi Lake cut a frustrated figure afterwards, but leaving Loftus Versfeld with something to show for their efforts was a solid start.
Home results at Brewery Field will determine whether Mark Jones’ side have a successful season but their opening performance on the road gave reason for optimism.
Ospreys have a formidable pack but it was their enterprise that stood out against Bulls, with four of their six tries coming in a superb first-half display.
They set the tone early with a strike play to put Keelan Giles over and there were prominent performances from wing Dan Kasende and the midfield of Phil Cokanasiga and two-try centre Kieran Williams.
Add in the playmaking of Dan Edwards and Jack Walsh, plus the threat from back-rowers on the edges, and there is plenty of promise with ball in hand.
Ospreys made 12 clean breaks to six by Bulls but did allow their hosts to put the squeeze on and did not hit their usual standards at the set-piece.
“There was a lot of self-harm with how we encouraged the Bulls into our red zone,” admitted head coach Mark Jones.
“With a side as good as the Bulls at this altitude it was always going to tell and we spent too much time without the ball.”
Ospreys face Stormers in Cape Town on Friday with Jones pledging they “won’t be trying to reinvent the wheel” against hosts who hammered Leinster 35-0.