Recent advances in large text-conditional image generative models such as Stable Diffusion, Midjourney, and DALL-E 3 have revolutionized the field of image generation, allowing users to produce high-quality, realistic images from textual prompts. While these developments have enhanced artistic creation and visual communication, they also present an underexplored attack opportunity: the possibility of inducing biases by an adversary into the generated images for malicious intentions, e.g., to influence society and spread propaganda. In this paper, we demonstrate the possibility of such a bias injection threat by an adversary who backdoors such models with a small number of malicious data samples; the implemented backdoor is activated when special triggers exist in the input prompt of the backdoored models. On the other hand, the model's utility is preserved in the absence of the triggers, making the attack highly undetectable. We present a novel framework that enables efficient generation of poisoning samples with composite (multi-word) triggers for such an attack. Our extensive experiments using over 1 million generated images and against hundreds of fine-tuned models demonstrate the feasibility of the presented backdoor attack. We illustrate how these biases can bypass conventional detection mechanisms, highlighting the challenges in proving the existence of biases within operational constraints. Our cost analysis confirms the low financial barrier to executing such attacks, underscoring the need for robust defensive strategies against such vulnerabilities in text-to-image generation models.