Unfortunately, because you undergrad major isn't CompSci, you are going to have a harder time sitting for the exam. You will have to get in course by course, most likely under the "engineering" track, which I think requires 42 hours of course work, including 8 hours of Calc based Physics with a lab (note: if you AP'ed out of Calc based Physics, you might be in trouble because you don't have the lab requirement). Some of your CompSci class might qualify, some may not. You really need to check out, and read carefully, the qualifications to sit for the exam on uspto.gov. EE or CompEng degree is very highly sought after. CompSci I'm not too sure about. I know in interviews I was often asked how much hardware engineering I remembered (I have a CompEng Masters with Software Engineering work experience). Honestly, if you want to go joint, I might think about doing Comp Engineering instead (if available). More of your classes will qualify for the patent exam, plus it will be good for you to get some hardware exposure. I didn't have trouble finding a great job, even in this economy, due to my background (My school and grades are very good, but not excellent. my numbers coming in were 3.87/164).
In the interest of saving some space I had the same question but with a BS and MS in Chemical Engineering. Should have the patent bar done by September when I start school. I've narrowed it down to Temple, Brooklyn, or Drexel (I'm intrigued by the co-op program and liked the school)
Also while were at it, does anyone know any schools that offer joint JD Masters of engineering program. I know Syracuse does. What other schools do?