Gloss is a written approximation that bridges Sign Language (SL) and its corresponding spoken language. Despite a deaf and hard-of-hearing population of at least 3 million in Bangladesh, Bangla Sign Language (BdSL) remains largely understudied, with no prior work on Bangla text-to-gloss translation and no publicly available datasets. To address this gap, we construct the first Bangla text-to-gloss dataset, consisting of 1,000 manually annotated and 4,000 synthetically generated Bangla sentence-gloss pairs, along with 159 expert human-annotated pairs used as a test set. Our experimental framework performs a comparative analysis between several fine-tuned open-source models and a leading closed-source LLM to evaluate their performance in low-resource BdSL translation. GPT-5.4 achieves the best overall performance, while a fine-tuned mBART model performs competitively despite being approximately 100% smaller. Qwen-3 outperforms all other models in human evaluation. This work introduces the first dataset and trained model for Bangla text-to-gloss translation. It also demonstrates the effectiveness of systematically generated synthetic data for addressing challenges in low-resource sign language translation.