1) 'Typical' CS masters program. (1-1.5 years) Accepts students with the requisite Undergraduate CS experience. (eg. at least Intro to CS, Data Structures, and Computation)
2) The Undergraduate CS Masters degree: (2-3 years) For Students with no CS/programming experience This is basically an undergraduate CS degree, only it counts as a Masters.
3) Mixed Program: (2.5-3 years) A masters in CS, with the concomitant courses, but requires you to take the undergraduate courses first, which may tack on 1.5 -2 years by my estimate of your situation.
Option 1) is not a likely option for you. If you manage to get accepted to one of these schools, you will be looking at 3) Mixed Program.
Option 2) is a good choice if you are pressed on time or finances, and want the prestige of a Masters degree, and don't care too much about taking Masters-level CS courses.
Another option is to get your second bachelor's in CS. Which is basically Option 2) but you don't get to call it a Masters.
One recommendation: A lot of the upper CS courses have prerequisites- namely Intro to CS and Data Structures, as well as Calc I and Calc II.
You could take these at the college if need be but IMHO you could and should learn these subjects through self-study, because you'll save money and time. Then when you enter University you can hit the ground running with the more advanced courses.