But things could have been much worse for the hosts had fly-half Alberto Di Bernardo not missed a touchline conversion following Dean Budd's late try - which competed his hat-trick.
Paddy Jackson's form with the boot was a positive for Mark Anscombe's men, the Irish fly-half kicking 19 points around tries from Andrew Trimble and Stuart Olding.
But Bowe admits he can't wait to get back on the field to bolster his side's chances of finishing top of the RaboDirect PRO12.
"For the moment I'm just concentrating on getting back on the field with Ulster with, hopefully, lots still to play for," he told The Irish Times.
But while Bowe, who played every minute of the Lions' Test series in South Africa four years ago, is expected to return from a knee injury before the season is out he accepts the chances of heading to Australia this summer appear forlorn.
"I think the odds are stacked against me at the minute, to be honest," added Bowe.
"It was amazing to be involved in the last Lions tour to South Africa. You never know what will happen."
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