You want to keep references to depression in, but you don't want her to read it.

I don't see a solution other than choosing one or the other. Either referring to depression as something more general, like 'difficult life experiences' or 'periods of personal growth', or letting her read it as-is.

Or, is there some way to say that your personal statement is SO extremely personal that you are not willing to share it, and some other way she could feel like she knows the non-academic you. Could the two of you meet to talk so she has a better picture of you to make her decision about writing a letter of recommendation?