The decision to change the alternator was taken on the basis that the alternator was bad and needed to be changed.
If you and the customer still believe the alternator was bad, then it is indeed a valid charge.
I would get it tested a couple more times and if the results are that it was right to change it, then you can go back and tell her that it needed to be changed anyway otherwise she would have become stranded at any moment.
Then tell her you changed the transmission fluid to try and fix the noise but it didn't work and you didn't ask so you're not charging her.
On the other hand, if you believe she won't be reasonable to your alternator explanation and your friendship means more to you, then don't explain anything and just tell her it was your mistake so you're not charging her.
If you and the customer still believe the alternator was bad, then it is indeed a valid charge.
I would get it tested a couple more times and if the results are that it was right to change it, then you can go back and tell her that it needed to be changed anyway otherwise she would have become stranded at any moment.
Then tell her you changed the transmission fluid to try and fix the noise but it didn't work and you didn't ask so you're not charging her.
On the other hand, if you believe she won't be reasonable to your alternator explanation and your friendship means more to you, then don't explain anything and just tell her it was your mistake so you're not charging her.