Ulster have not got their hands on the league trophy since the 2005-2006 season with an 24-18 loss to Leinster two years ago the closest they have come in recent times.
They are well placed for another tilt at the play-offs this season though, sitting second in the table with four matches remaining of the regular season.
Winger Bowe himself has not turned out for the side since January due to international commitments with Ireland.
But fresh from his first week back training with the club, the 31-year-old has his eyes firmly on an extended season, culminating in running out for the final next month.
"It's great to be back. It has been a super time down with the Irish squad, but I'm glad to be back with the Ulster lads," Bowe told Ulster's official website.
"Everyone is in great form. It was good to get the bonus points last weekend and everyone is excited about the next couple of months with some massive games ahead.
"We are in a great place in the league with all the top teams to play. Obviously the guys who have been playing in recent weeks have gone really well and we know that there is going to be competition for places.
"This is moving into the business end of the season. We have had an up and down season in different parts.
"We know that the final of the league will be at Kingspan Stadium. It is an enormous incentive for us to aim for. We want to be playing in a final at home and I think that we have that all in our own hands."
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