How do I get into a Computer Science Masters without an undergrad in CS?

Many schools will require you to take remediation courses if they do not feel you meet the course requirements for the graduate program. They will be fairly upfront about what they think you would need, but it will mean taking more Bachelors level classes at cost before being accepted to the program.

In general I would show any additional work you have done to improve your programming skills, including code you have written.

A lot of qualified people do not apply to top schools (I.E. MIT) because they do not believe they would get in. But I would not recommend focusing on any one school and instead find a few programs you like and apply to all of them.

Some schools will allow you to take classes as a non-degree seeking student, which would provide both a way to prove yourself and also gauge the program and its suitability to you. I would check with the program to see how many credits they accept through this method though.

As an aside, I am in the same boat. I majored in Mathematics with a minor in Physics but have been working as a programmer for the last three years. I am now looking into online masters programs in Computer Engineering or Computer Science.

Many departments do not require you have a Bachelor's in CS to pursue graduate studies. They might have a stipulation of a minor in CS, though. You'd have to check with the individual departments. Bioinformatics is similar to CS in some schools, so they may waive that minimum requirement. The main reason for their requiring a minor is to ensure you've had a sufficient foundation to build upon. Taking more courses in a local school first would fill any gaps you have.

In the end, it comes down to what the department says. Contact some of the ones you like and see what they say. They may want you to take more math, for instance, over anything else.

Edit: Removed statement about GRE subject test in CS.