Who ruled India in the time of the Buddha and Mahavira?

Around 2,500 years ago northern India was not one country but a patchwork. The Mahajanapadas were sixteen kingdoms and aristocratic republics that existed in ancient India from the sixth to fourth centuries BCE. Some were kingdoms and some were republics: Vajji, a confederacy of clans with its capital at Vaishali, is indicated to have been a republic.

It was a time of change. The 6th and 5th centuries BCE are often regarded as a major turning point: India's first large cities since the Indus Valley Civilisation arose, along with the śramaṇa movements, including Buddhism and Jainism, which challenged the religious orthodoxy of the Vedic period. Mahavira, considered by Jains to be the 24th and final Tirthankara of the current time cycle, belongs to that world. His historicity is well established among scholars, though the dates of his life are uncertain.

Meanwhile one state pulled ahead. In the struggle for supremacy, the growing state of the Magadhas emerged as the predominant power, annexing several other janapadas. Its rulers Bimbisara and his son Ajatashatru are mentioned in Buddhist and Jain literature as contemporaries of the Buddha and Mahavira.

We should be careful with the details. Buddhist and other texts refer only incidentally to the sixteen great nations and give no connected history except for Magadha, and a Jain text gives a different list. History here is stitched together from religious writings.