Can I use bc pill to ease into menopause?

Yes. Some will use bcp up until age 55 in healthy non smoking women. This will help symptoms. The pill free week or "cycle" week, blank pills etc., is a time where symptoms will occur. Therefore, to benefit most from this therapy, one should use the pill continuously without breaks or cycles. At some point though, transition to traditional post menopausal hormone replacement should occur.
Not recommended. The birth control pill contains non-bioidentical hormones and increases coagulation and inflammatory factors due to digestion in the liver. Menopause should be treated with topical, cyclic, bioidentical hrt.