* Starting a new program: This is the most common route. You would apply to a university offering a Bachelor of Science program in a field of your choosing and begin the program from scratch. Some credits from your BA *might* transfer, depending on the universities and the specific courses. You would need to contact the university's admissions office to find out how many credits would transfer and whether that would shorten your degree timeline.
* Completing a second bachelor's degree: This is essentially the same as the first option, but emphasizes that it's a completely separate degree program.
In short, you can't upgrade or add a BS to your existing BA. You need to pursue a new, separate BS degree program. The extent to which prior credits transfer depends on the institutions involved.