Objectives Vaccination rollout against COVID-19 has started in developed countries in early December 2020. Mass immunization for poor or low-income countries is quite challenging before 2023. Being a lower–middle-income country, Bangladesh has begun a nationwide COVID-19 vaccination drive in early February 2021. Here, we aimed to assess the opinions, experiences, and adverse events of the COVID-19 vaccination in Bangladesh. Methods We conducted this online cross-sectional study from 10 February 2021, to 10 March 2021, in Bangladesh. A self-reported semi-structured survey questionnaire was used using Google forms. We recorded demographics, disease history, medication records, opinions and experiences of vaccination, and associated adverse events symptoms. Results We observed leading comorbid diseases were hypertension (25.9%), diabetes (21.1%), heart diseases (9.3%), and asthma (8.7%). The most frequently reported adverse events were injection site pain (34.3%), fever (32.6%), headache (20.2%), fatigue (16.6%), and cold feeling (15.4%). The chances of having adverse events were significantly higher in males than females ( p = 0.039). However, 36.4% of respondents reported no adverse events. Adverse events usually appeared after 12 h and went way within 48 h of vaccination. Besides, 85.5% were happy with the overall vaccination management, while 88.0% of the respondents recommended the COVID-19 vaccine for others for early immunization. Conclusion According to the present findings, reported adverse events after the doses of Covishield in Bangladesh were non-serious and temporary. In Bangladesh, the early vaccination against COVID-19 was possible due to its prudent vaccine deal, previous mass vaccination experience, and vaccine diplomacy.