California CLS here. You can major in anything you want as long as take the required courses to apply for a CLS program. Health Sciences and Microbiology are good majors since most if not all the major required courses fulfill the CLS program requirements. I suggest you get your BS degree and apply to the year long CLS program. The CLS programs are competitive especially in California, so make sure you do well in the pre-req classes in college.
Many of the Cal States: SDSU/SFSU/CSULA/CSUGH/SJSU will have science majors with an emphasis or option in CLS. If you have any specific quesitions, you can PM me. Good Luck
http://www.csubiocompass.org/lifescienceeducation/clinicalsciencescertificates.html
http://www.csubiocompass.org/lifescienceeducation/clinicalsciencesdegrees.html