It’s tough to end a relationship with someone you have a history with. Having a “breakup” conversation with your friend may make her defensive and uncomfortable and going MIA and avoiding her calls may be confusing and hurtful. The reality is that no matter how you approach it, there’s a good chance you may hurt her feelings (unless she also feels that you don’t relate to each other anymore, which is entirely possible).
If you’re going to have a talk, frame it in terms of your needs and try not to attack her character or blame her for the reason you’re not available to be her friend. You can say, “My schedule is so busy these days, I don’t feel I have the time to give enough attention to this friendship. Of course I wish you the best but need to be honest with you that I’m not really available to spend time with you…” Or you can tell her that as hard as it is to admit, you realize that you’re in a different phase of your life and feel that you’ve grown apart.
Show don’t tell.
Your other option is showing her through actions, and not words, that you aren’t available. She may take the hint if you never initiate plans or take a while to get back to her.
The bottom line is that a relationship must be reciprocal. It won’t work if one person doesn’t want to be there.