College Opportunities for Servicemembers Act This bill authorizes the Department of Defense to conduct outreach to institutions of higher education for purposes of entering into more agreements that may provide training or internships to members of the Armed Forces under the Skillbridge program. Skillbridge provides members of the Armed Forces with opportunities to gain civilian work experience through training, apprenticeships, or internships and connects service members who are transitioning to civilian life with job experiences. Additionally, DOD may conduct outreach and provide assistance to institutions of higher education to support the creation of centers at the institutions through which members of the Armed Forces who are eligible for Skillbridge and veterans may receive job training.