Hi bleeding can happen within 6 months of starting any new hrt, so there is usually no need for investigations unless it continues after this time.
I have had tests twice for post menopausal bleeding and the endometrium was 9mm and then 6mm. Both times all tests were normal and it was just put down to being “one of those things.”
It could also,be that your body is not ready for continuous hrt. Some ladies are still having periods in their late 50s. x