Consider taking some EE classes as a non-degree student. The schools that require a BS in EE are looking to make sure that you have the background for grad work.
Consider something like Boston University's LEAP program, which is for students who majored in non-sci/eng fields who want to get graduate degrees in engineering. From their website:
"Phase I of LEAP consists of a core set of about ten to twelve discipline-related undergraduate courses. Credit is given for prior equivalent coursework. These courses do not lead to a BS degree, but will qualify you for entry into the graduate phase of LEAP.Phase II consists of our regular Master's program in any of seven engineering disciplines. Many LEAP students go on to doctoral studies at Boston University."
A few universities have post-bac programs in EE, also intended for people who didn't major in it. Tufts University, for example, has a certificate program in Microwave Engineering.
