Budgeting for Opioid Addiction Treatment Act This bill amends the Internal Revenue Code, with respect to excise taxes on manufacturers, to impose a one cent per milligram fee on the sale of active opioids by the manufacturer, producer, or importer. The fee excludes prescription drugs used exclusively for the treatment of opioid addiction as part of a medically assisted treatment effort. The Department of Health and Human Services (HHS) must establish a program to provide rebates or discounts to cancer and hospice patients to ensure that they do not pay the fee. The bill amends the Public Health Service Act to require any increase in federal revenues from the fee after rebates and discounts are subtracted to be distributed to states under the Substance Abuse Prevention and Treatment Block Grant program. The states must use the funds exclusively for substance abuse (including opioid abuse) efforts in the states, including: (1) specified treatment programs, and (2) the recruitment and training of substance use disorder professionals to work in rural and medically underserved communities. HHS must report to Congress on the impact of this bill on the retail cost of opioids and patient access to opioid medication, the effectiveness of the discount or rebate for cancer and hospice patients, how the funds are being used to improve substance abuse treatment efforts, and suggestions for improving access to opioids for cancer and hospice patients and substance abuse treatment efforts.