Background: Globally, the COVID-19 pandemic seriously affected both physical and mental health conditions. This study aims to assess changes in the prevalence of depression among older adults during the COVID-19 pandemic in Bangladesh and explore the correlates of depression in pooled data. Methods: This study followed a repeated cross-sectional design and was conducted through telephone interviews on two successive occasions during the COVID-19 pandemic (October 2020 and September 2021) among 2077 (1032 in 2020-survey and 1045 in 2021-survey) older Bangladeshi adults aged 60 years and above. Depression was measured using the 15-item Geriatric Depression Scale (GDS-15). The binary logistic regression model was used to identify the factors associated with depression in pooled data. Results: A significant increase in the prevalence of depression was noted in the 2021 survey compared to the 2020 survey (47.2% versus 40.3%; adjusted odds ratio (aOR): 1.40, 95% confidence interval (CI): 1.11–1.75). Depression was significantly higher among participants without a partner (aOR 1.92, 95% CI 1.45–2.53), with a monthly family income of <5000 BDT (aOR: 2.65, 95% CI 1.82–3.86) or 5000–10 000 BDT (aOR: 1.30, 95% CI 1.03–1.65), living alone (aOR 2.24, 95% CI 1.40–3.61), feeling isolated (aOR 3.15, 95% CI 2.49–3.98), with poor memory/concentration (aOR 2.02, 95% CI 1.58–2.57), with non-communicable chronic conditions (aOR 1.34, 95% CI 1.06–1.69), overwhelmed by COVID-19 (aOR 1.54, 95% CI 1.18–2.00), having difficulty earning (aOR 1.49, 95% CI 1.15–1.92) or obtaining food (aOR 1.56, 95% CI 1.17–2.09) during COVID-19 pandemic, communicating less frequently (aOR 1.35, 95% CI 1.07–1.70) and needing extra care (aOR 2.28, 95% CI 1.75–2.96) during the pandemic. Conclusions: Policymakers and public health practitioners should provide immediate mental health support initiatives for this vulnerable population during the COVID-19 pandemic and beyond. Policymakers should also invest in creating safe places to practise mindful eating, exercise, or other refuelling activities as a means of preventing and managing depression.