Dense retrieval systems are commonly used for information retrieval (IR). They rely on learning text representations through an encoder and usually require supervised modeling via labelled data which can be costly to obtain or simply unavailable. In this study, we introduce a novel unsupervised text representation learning technique via instruction-tuning the pre-trained encoder-decoder large language model (LLM) under the dual-encoder retrieval framework. We demonstrate on multiple languages that the corpus representation can be augmented by the representations of relevant synthetic queries generated by the instruct-tuned LLM founded on the Rao-Blackwell theorem. Furthermore, we effectively align the query and corpus text representation with self-instruct tuning. We evaluate our proposed method under low-resource settings on three English, two German and one Portuguese retrieval datasets measuring NDCG@10, MRR@100, Recall@100. We significantly improve the average zero-shot retrieval performance on all metrics, increasing out-of-box FLAN-T5 model variations by [4.73%, 6.15%] in absolute NDCG@10 and exceeding four supervised dense retrievers.