The Irish side, who remain unbeaten so far this season, ran in four tries at Franklins Gardens in a heavy victory over the 2011 finalists.
With Ulster now looking towards a home quarter-final following a perfect start in the competition, Bowe knows that when it comes to qualification for the knockout stages, the hard work is not over yet.
"We know that Northampton are going to come to us this week and come at us twice as hard," said Bowe to the Northampton Chronicle.
"Yes we took a bonus point out of Franklin Gardens, but they (Northampton) made us work hard for that win.
"It was not until the final minute or two that we went in for the fourth try to secure that bonus.
"We can be massively pleased to have made it four wins on the bounce away from from home, but in terms of Europe, the job is only half done.
"We have to do it all again this week, and we will have to be up another per cent on our game again."
Gilbert has released a new line of rugby cleats. The Gilbert Virtuo 8S is part of the exciting new product. Check it out.
The entire All Blacks apparel line has been updated for 2013/14. Check out the New Zealand All Blacks polo.
The Nike Tiempo is a solid rugby cleat and one of few styles still made from full-grain natural leather.
The Gilbert Blitz 8S rugby cleat is a great cleat at a great price of $69.99. Get a new pair of cleats today.
A cool looking all black rugby cleat with the high performance adidas is known for. Get in the Gear!
Wear the crest of the British and Irish Lions on your t-shirt. A great look for the summer.
The All Blacks Performance t-shirt is black with hints of blue from the training jersey. Very Cool.
The New Zealand All Blacks training jersey for 2013/14. Get in the Gear!
The USA Rugby Pro Alternate rugby jersey is perfect for any fan of the Eagles. Get yours to wear during the summer Test matches.
The NEW All Blacks 2013/14 jersey has arrived at World Rugby Shop. Dare to wear the colors of the All Blacks.