I may be old fashioned, but I think it’s best to break the news face to face, if possible. Phone call is second best, and email or text is probably at the bottom of the list. It depends somewhat on how you normally communicate outside of lessons, etc. the “rules” have changed with all the new ways of communicating, but that’s my 2 cents.
Just tell her what you said here–that you have enjoyed these past six months, but you would like to try a different teacher. Then send a card in the mail expressing your appreciation. Anyone who teaches must be prepared for the eventuality of their students leaving them, so hopefully she will know how to handle it with grace.
Good luck. 🙂