It would be a real shame to miss out on the benefits of hormone therapy due to bleeding - this can easily be managed.
Firstly if the mini pill you were taking was desogestrel, you can take this alongside HRT. You don't have to choose. If this was keeping you bleed free, continuous progesterone would be more appropriate than cyclical - the latter is designed to induce bleeding.
Other bleed free options include a combined oral contraceptive pill taken continuously, for example I take Zoely.
Alternatively, and this is off label but increasingly popular and supported by evidence, is using two desogestrel pills taken every day as the progestogen component of hormone therapy.
A mirena IUS can also be a good option for achieving amenorrhea or at least minimal bleeding.
Do speak to your doctor about treatment that offers bleed control as well as estrogen replacement - many women are made to feel that they just have to put up with bleeding but this is not the case.