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 very limited prior work on Bangla text-to-gloss translation and no publicly available parallel dataset at the time of this work. To address this gap, we construct the first publicly available 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 automatic metric scores, while open-source models perform competitively despite being much smaller. This work introduces the first publicly available expert-annotated Bangla text-to-gloss dataset, benchmark 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.