Should a undergraduate rely on PhD students to publish papers or do it individually?
One alternate strategy that could help is to see about trying to present a poster of your work at a conference. Even if that doesn't have quite the same prestige as a paper in a journal or an accepted paper at a conference (if you're in CS), it still is a sign of doing significant amounts of research. An especially good sign would be if you could win a "best student poster" or "best student talk"-type award. 

However, the important thing for you will be to be able to discuss what you have done with authority in your statement of purpose to graduate schools, and to get a good letter of recommendation from your advisor that clearly outlines your contributions to your project. Having a publication is nice, but it's not an essential component for graduate school admissions.