A Study to Assess Adverse Events, Change in Disease Activity and How Intravenous (IV) ABBV901 Moves Through the Body Alone or in Combination With Bevacizumab in Adult Participants With Ovarian Cancer

Inclusion Criteria: * Diagnosis of an advanced or unresectable malignant high grade serous epithelial ovarian, fallopian tube, and primary peritoneal cancers (EOC), fallopian tube or primary peritoneal cancer by histology (World Health Organization \[WHO\] criteria). * Participants must be considered platinum resistant or platinum ineligible. Platinum resistant disease is defined as radiographic progression within 6 months (up to 182 days) after the last dose of the most recent platinum therapy). * Prior anticancer therapy: * Must have received appropriate standard of care therapy and be appropriate for participation in a Phase I study in the opinion of the investigator. * Platinum-resistant, high grade serous EOC cannot have had more than 2 prior lines of therapy, since the development of platinum resistance or ineligibility. * For participants enrolled in backfill, subjects must provide consent to paired biopsies which are pretreatment and on-treatment tumor biopsies from the same tumor lesion. Exclusion Criteria: * Ovarian Cancer (OC) with histologies other than high grade serous OC including endometrioid, low grade, clear cell, mucinous, or borderline ovarian tumor. * Prior therapy with an antibody-drug conjugate containing a topoisomerase inhibitor. * Prior history of Grade \>= 2 ILD or pneumonitis. * History of interstitial lung disease (ILD) or pneumonitis that required treatment with systemic steroids, or any evidence of active ILD or pneumonitis on Screening chest computed tomography (CT) scan. * Must not have systemically used known strong cytochrome P450 (CYP)3A inhibitors or inducers within 14 days or 5 half-lives of the drug (whichever is shorter) prior to the first dose of the study drug through the end of the DLT observation period. If clinically indicated, strong CYP3A inhibitors and inducers may be used with caution after the dose-limiting toxicity (DLT) period.