Not Bear, but Bare Bare my soul. <= this means to expose your soul for inspection. To show your true self. Earn my stripes <= this phrase is taken from the military where you are awarded strips on your uniform as you progress in rank. So to earn your strips is to earn your rank, or earn your position.

To "bear my soul" or "bear one's soul" means to share inner thoughts or feelings, usually private ones. Example: They're friends, but she would not bear her soul to him. To "earn my stripes" or to "earn one's stripes" means to put in hard work and experience in order to earn a position. Example: She earned her stripes as a teacher before becoming a principal.