B-On-Time Student Loan Relief Act of 2014 - Amends title IV (Student Assistance) of the Higher Education Act of 1965 to direct the Secretary of Education to award interest-free loans to students who meet any prerequisites that the Secretary requires.

Requires eligible students, at a minimum, to:

• have either graduated on or after the 2013-2014 school year from a secondary school in the United States, one operated by the Department of Defense (DOD), or its equivalent or earned an associate's degree from an institution of higher education (IHE) on or after May 1, 2013;
• have not earned a bachelor's degree;
• be enrolled on a full-time basis in an IHE undergraduate degree or certificate program; and
• have completed a Free Application for Federal Student Aid (FAFSA) and met the eligibility requirements for title IV assistance.

Directs the Secretary to forgive students' outstanding principal on such interest-free loans if they:

• receive a bachelor's degree within a set timeframe, determined by the Secretary;
• maintained a certain grade point average or majored in a science, technology, engineering, or mathematics (STEM) field while enrolled in the IHE; and
• meet any other requirements established by the Secretary.

Requires the Secretary to award such loans and grant such loan forgiveness on a first-come, first-served basis, subject to the availability of appropriations.