In a period of feisty Irish derbies, Leinster are looking to bounce back from defeat to Munster at Thomond Park on Boxing Day.
Bowe expects Matt O'Connor's men to come out firing at the RDS when Ulster are the visitors on Saturday.
However, he also believes the Ulstermen are due some success against the three-time European champions and four-time winners of the PRO12.
"Leinster have been the best team for the last few years and our record against them hasn't been great," Bowe told the Belfast Newsletter.
"We have been so close to winning competitions and have been knocking on the door.
"Unfortunately we kept coming up against them and that was the end of it for us and that is very frustrating for us as players, supporters and people involved with Ulster Rugby.
"We are very positive about our chances this weekend, I think it is safe to say both sides aren't playing as good as rugby as they would like to at the minute.
"The two teams have been battling it out the last few years, Leinster will be hurting from last week and will want to come out with a big performance this weekend.
"Leinster against Ulster is always a packed house. It's one, as players, that is not very hard to get up for.
"It is always brilliant to get one over on the guys you know so well. We haven't had too much luck in doing that over the last couple of years but this is a great opportunity for us to make a big statement for the rest of the season."
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