An increasing reliance on recommender systems has led to concerns about the creation of filter bubbles on social media, especially on short video platforms like TikTok. However, their formation is still not entirely understood due to the complex dynamics between recommendation algorithms and user feedback. In this paper, we aim to shed light on these dynamics using a large language model-based simulation framework. Our work employs real-world short-video data containing rich video content information and detailed user-agents to realistically simulate the recommendation-feedback cycle. Through large-scale simulations, we demonstrate that LLMs can replicate real-world user-recommender interactions, uncovering key mechanisms driving filter bubble formation. We identify critical factors, such as demographic features and category attraction that exacerbate content homogenization. To mitigate this, we design and test interventions including various cold-start and feedback weighting strategies, showing measurable reductions in filter bubble effects. Our framework enables rapid prototyping of recommendation strategies, offering actionable solutions to enhance content diversity in real-world systems. Furthermore, we analyze how LLM-inherent biases may propagate through recommendations, proposing safeguards to promote equity for vulnerable groups, such as women and low-income populations. By examining the interplay between recommendation and LLM agents, this work advances a deeper understanding of algorithmic bias and provides practical tools to promote inclusive digital spaces.