Back to Work Bonus Act This bill eliminates Federal Pandemic Unemployment Compensation, provides for direct payments to individuals who begin work with a new employer, and otherwise addresses COVID-19 pandemic-related unemployment benefits. Specifically, the bill allows states to provide a direct payment to individuals who are eligible for Federal Pandemic Unemployment Compensation (an additional payment for those already receiving a weekly unemployment benefit) but who lose that eligibility subsequent to the bill's enactment due to commencing employment with a new employer. An individual must continue employment with the new employer for at least 4 weeks to be eligible for the $900 payment under the bill. This bonus payment is only available for nongovernmental employment commencing prior to August 14, 2021. Payments made by states under the bill are eligible for 100% federal reimbursement in the same manner as Federal Pandemic Unemployment Compensation. The bill also ends Federal Pandemic Unemployment Compensation upon enactment. Currently, it is set to end September 6, 2021. Finally, the bill modifies work search requirements for claimants to receive Pandemic Unemployment Assistance so that an individual is excused from current availability or ability to work requirements for reasons related to COVID-19 only if the individual (1) has an active COVID-19 infection, (2) is ordered quarantined, or (3) has caregiving duties due to a COVID-19 infection or quarantine. (Pandemic Unemployment Assistance is a temporary federal program for individuals who are not otherwise eligible for unemployment benefits and are unemployed, partially employed, or unable to work for reasons related to COVID-19.)