Benetton Treviso have yet to pick up a point in the Pool, but Bowe knows better than to write them off as no-hopers. After all, Franco Smith's men earned a draw at Ravenhill last season and only lost to Ulster by a point at home in their domestic league matches.
But if Ulster can put two more wins together then they will be well on their way to qualifying for the knock-out stages for a third successive season.
"It was an amazing result for us at the weekend. It is such a tough place to go to and Montpellier were unbeaten at home this year," said Bowe in the wake of his side's 25-8 triumph at Stade Yves du Manoir.
"There is a lot of belief in this Ulster team that we can take on the best teams and credit to the forwards today for taking on a ferocious home pack. They stuck it up to them.
"We were clinical and, even though we only scored one try, we cut out the penalties. Our work in the breakdown was the most important thing and as we kept the scoreboard ticking over you could hear the Montpellier guys losing their rag a bit
"We know exactly what Treviso are like in the PRO12 and they gave Montpellier a tough game in round one. We know they will be very difficult away from home, but we will be targeting two wins to try to set us up in the Pool."
The win in Montpellier was Ulster's second in a row on French soil in the Heineken Cup and made it five on the trot this season. Their eight points from their opening two matches has given them a two point cushion at the top of the Pool over the Tigers, who snatched a try bonus with the last play of the game against Benetton Treviso at home lst weekend.
"It is going to be a difficult task going to Welford Road in Round 6 and we know this Pool is far from being over. But we're very happy with the way we stand so far," added Bowe.
"We still have huge amounts to work on. We are creating lots of chances, but we aren't putting enough of them away.
"That's something we need to work on. We created lots of opportunities against Leicester, but silly errors stopped us converting them. It is in the big games that you need to be more clinical."