Is there a Buddhist scripture in Southern Buddhism (Hinayana) that says that there is no Buddha in the south to live in bliss?

No. There is a mention of chanting Buddha in the six or ten chanting of Buddhism. But this chanting is based on remembering the top ten names of the Buddha (think about how the Buddha got these top ten names). Thirty-two adults fall in love, and seventy adults accompany them. The only Buddha at the top of the throne is Sakyamuni Buddha. All other buddhas are past buddhas and have nothing to do with this world. One Buddha is all Buddhas. Amitabha Hokkekyo and Amitabha Hokkekyo, which have been circulating in the south for a long time, are basically the same except for the famous passages of Amitabha. Southern Communication encourages individual practice. Individuals can only help others if they reach the realm of enlightenment, otherwise it is nonsense. Buddhism does not advocate inferior "immigration thought". There are still half-robbed Maitreya Buddhas in the world, pure land on earth, and all people become Buddhas. Why should we "immigrate" to the West and wait for billions to become a Buddha?