I think schools have partnered with bicycle companies in the past to reduce the cost of the bicycles in exchange for the exposure. I'm not sure extra advertisements would work-you want to give students something they want to ride, and covering a bicycle with ads might make you look "different and weird."
UND has tried the "green bikes" (shared bicycle program) thing a couple times in the last five years, with little success because there was no oversight and most of the bikes ended up either off-campus or tossed in the coulee. This was also attempted at my undergrad, unfortunately the same thing happened and they moved the program to be an extension of the library, where you could "borrow" a bicycle on your student ID card.
That being said, I don't think bicycle access is the problem, and I don't want this idea to be about getting bicycles to people who can't otherwise get them. It's more along the lines of encouraging people to give up their car for a year and see what happens. There are full racks all over campus, and I'm pretty sure a large number of bicycles are just left behind at the end of the year, to get cut off and sold at the police auction, so finding a ride isn't the problem for the average student, it's breaking that automobile dependence.