The rapid expansion of the digital world has propelled sentiment analysis into a critical tool across diverse sectors such as marketing, politics, customer service, and healthcare. While there have been significant advancements in sentiment analysis for widely spoken languages, low-resource languages, such as Bangla, remain largely under-researched due to resource constraints. Furthermore, the recent unprecedented performance of Large Language Models (LLMs) in various applications highlights the need to evaluate them in the context of low-resource languages. In this study, we present a sizeable manually annotated dataset encompassing 33,605 Bangla news tweets and Facebook comments. We also investigate zero- and few-shot in-context learning with several language models, including Flan-T5, GPT-4, and Bloomz, offering a comparative analysis against fine-tuned models. Our findings suggest that monolingual transformer-based models consistently outperform other models, even in zero and few-shot scenarios. To foster continued exploration, we intend to make this dataset and our research tools publicly available to the broader research community. In the spirit of further research, we plan to make this dataset and our experimental resources publicly accessible to the wider research community.