Its really according to how your mom is girly, I hope for u she is understanding and gentle with u. first ask her to have empathy for u before u start. ( put herself in your shoes). tell her to pretend she is u approaching her right at that moment with this important thing and that right then, she is her terrified daughter coming to her. thats what i always do when my kids come to me. i try to feel what they are feeling. then take a deep breath and spit it out. Being a mom I can tell u, she will always love u no matter what u have to tell her.
if you can, take her out somewhere, that way she will be least likely to yell at you in public. just tell her you need to tell her something. tell her and then say how truly sorry you are. best of luck!
Oh sweetie it's hard because you feel you disappointed them. Maybe you did BUT.... She is your mother. She loves YOU unconditionally. That means she will get over it! She will be on your side. She will help you with your problem and be there for you as long as she lives. Just do it.