OP, I was in such a position as you describe. My undergraduate background is in Economics, and I will be attending school for an MS in CS program. I think you need to play your strengths: undoubtedly you have very strong quantitative and reasoning skills (given your major), be sure to communicate that as clearly as you can. In the meantime, I think work experience is a factor that can work in your favor. Look for opportunities to get involved in programming roles, or a role that uses computation skills heavily (data analysis of some sort might be something to look into). Then you can leverage this in your SOP. Be sure to research programs, there are various programs out there who are quite lenient with prereqs (as in, they will accept you into their program and then require you to make up whatever formal background you are missing). Best of luck!