It's possible to cover all of the prerequisites in one year provided that you are comfortable enough with programming, the basics of data structures and math to jump straight into upper-level coursework. Otherwise it might still be doable, but crucially dependent on whether all courses are offered in the "right" semester.
Here's a short list of courses that's frequently required for admission to Master's programs in computer science:
One CS theory course (analysis of algorithms or theory of computation)
Preferably: Linear Algebra
If you have some idea which university you'd like to attend, I'd encourage you to ask them about their admission policies directly.
Going back for a second bachelor's is not really something I'm considering, 4 years is a bigge.
Some universities will give you a 2nd Bachelor's degree for completing the requirements for another major; they would transfer all of the general education courses and free electives from your first degree. That means you could get another Bachelor's degree in 1-2 years - certainly worth looking into.
Another option are Master's programs in computer science that are specifically targeted at career changers and will teach you the prerequisite undergraduate material. Penn has one of those: Penn CIS