Oh, come on, just start talking about it as you did in your post. Don't go memorizing words. Quietly, nicely, something like you said here -
You said I only tell you the basics... I realize that you are right.
"And now that i think of it there are many things going on in my life or have happened yet she doesnt know about it."
Don't drag the friend into it. Let your girlfriend tell you about her mother if and when she feels like it. Don't mention it, that is for her to tell when she decides to.
Don't expect trust to happen in five minutes. Just be straightforward when the opportunity happens and you feel like telling stuff.