Inclusion Criteria:  Women who report vasomotor symptoms (hot flashes or night sweats or both). No menstrual periods for at least 60 days. Age 45-65. Women age 45-49 with prior hysterectomy or endometrial ablation with rare or no periods due to ablation must have a Follicle Stimulating Hormone (FSH) of 25 mIU/ml or higher to be eligible. BMI <36 kg/m2  Risk Factors/Level. Moderate risk of developing breast cancer based on either by having any one or more of the following:  First or 2nd degree relative with breast cancer Known carrier of moderate to high penetrance germline mutation Prior breast biopsy showing proliferative breast disease or multiple prior biopsies High mammographic density (Volpara® categories c or d or BIRADS density assessment as heterogeneously or extremely dense (c or d). IBIS Breast Cancer Risk Evaluation Version 8 (http://www.emstrials.org/riskevaluator/). 10-year relative risk of >2X that for the population for age group. Prior mammogram must have at least a Volpara® fibroglandular volume of 80 cm3 or BIRADs b, c, or d category density and/or investigator estimated visual dense area of at least 25%. The entire breast must be incorporated in a single view for both the right and left breast. (i.e., women whose breasts are so large that the images must be captured as a mosaic are not eligible). If no prior mammogram, but breast density is readily appreciated and documented on physical exam, a study-provided 3D mammogram with Volpara® software must be performed to document above eligibility criterion. It will then constitute the baseline mammogram.  Willing to comply with study procedures:  Have blood drawn for screening tests - comprehensive metabolic panel (plus FSH if age 45-49 and no uterus or endometrial ablation) Have blood drawn to archive serum for assay of estradiol, testosterone, progesterone, sex hormone binding globulin (SHBG), FSH at baseline and 6-month visits (and 12 months for women originally randomized to wait list control and subsequently taking BZA+CE for the next 6 months). Undergo a history, physical, and breast exam at baseline and 6-month visits (and 12 months for women originally randomized to wait list control and subsequently taking BZA+CE for the next 6 months). History, physical exam and breast exam performed by a study-associated clinician within 3 months prior to enrollment may be substituted for baseline evaluations. Have a mammogram at University of Kansas Medical Center (KUMC) with Volpara® volumetric density at baseline and 6-month visits (and 12 months for women originally randomized to wait list control and subsequently taking BZA+CE for the next 6 months). Have a study provided abbreviated MRI at KUMC at baseline and 6-month visits. Be contacted by the trial coordinator by phone, email, or text at months 1 and 3 (and months 7 and 9 for women originally randomized to wait list control and subsequently taking BZA+CE for the next 6 months). Complete Mayo Clinic hot flash assessment at baseline and 6-month visits (and month 12 for women originally randomized to wait list control and subsequently taking BZA+CE for the next 6 months). Women 45-55 with a functional uterus (e.g., no prior endometrial ablation), menstrual period in the past 12 months, and heterosexually active, must be agreeable to use some non-hormonal form of contraception while taking BZA+CE unless husband or partner has had a vasectomy. Able to understand and sign an informed consent form for screening and for intervention. Participants on the optional random periareolar fine needle aspiration (RPFNA) procedures must meet eligibility criteria for participation on HSC4601, Breast Random Fine Needle Aspiration and/or Nipple Aspirate Fluid Collection of Breast Tissue to Aid in Short-term Risk Assessment. Participants must sign a separate optional consent for this study as well as for HSC4601. However, any eligibility criteria dealing with hormone replacement therapy and SERMs are excluded to allow the 6-month aspiration. Comprehensive Metabolic Panel shows clinically acceptable renal and hepatic function lab values. For women with intact uterus and ovary(ies) and less than age 55, a negative pregnancy test is required.  Exclusion Criteria:  Risk: A prior biopsy showing pleomorphic lobular or ductal carcinoma in situ or invasive breast cancer.  Medical Conditions:  Have a predisposition to or prior history of thromboembolism, deep venous thrombosis, pulmonary embolism, or stroke History of renal or liver disease Prior invasive ovarian or endometrial cancer Any other condition or intercurrent illness that in the opinion of the investigator makes the woman a poor candidate for BZA+CE.  Medications  Taking systemic hormones within two months (eight weeks) prior to baseline MRI and mammogram. Taking systemic hormones within two months (eight weeks) prior to baseline MRI and mammogram. Taking tamoxifen, raloxifene, Duavee®, or any selective estrogen receptor modulator, or an aromatase inhibitor within 12 months prior to baseline MRI and mammogram.  Exclusion Criteria after baseline studies:  Mammogram with Volpara® software and/or abbreviated MRI interpreted as concerning for cancer - unless recommended breast biopsy has been performed and confirmed as benign. Dispensing of BZA+CE for those randomized to receive it immediately does not occur within 3 months of baseline MRI. Unwilling to comply with future study procedures. Started hormone replacement, selective estrogen receptor modulator, or aromatase inhibitor after baseline studies performed but prior to randomization.