Outpatient Therapy Modernization and Stabilization Act This bill modifies payment and funding for certain outpatient therapy services under Medicare. Among other things, the bill specifically includes physicians, physical therapists, occupational therapists, and other specified practitioners who are enrolled as Medicare suppliers as eligible suppliers who may receive COVID-19 (i.e., coronavirus disease 2019) relief funds under the Public Health and Social Services Emergency Fund. The bill also permanently allows physical therapists, occupational therapists, and speech-language pathologists to provide telehealth services under Medicare, and includes specified therapy services as eligible Medicare telehealth services. (Currently, the Centers for Medicare & Medicaid Services is authorized to waive requirements for Medicare telehealth services during the public health emergency relating to COVID-19, and it has done so to allow all providers that are otherwise eligible to furnish in-person services under Medicare to also furnish telehealth services.)