Roughly it means you survived the situation. The word "bare" means "to be exposed, or uncovered to your environment", or pretty much, Naked. To bare through something means to accomplish your goal despite being in a really bad position.
For example, if you had just a weekend to write a 20-page essay, study for a few exams, and do some additional homework... After you survived this tormenting weekend, you could say "I bared (bore?) through it."