Baba Bhagirath Varni was born in 1868 at Mathura and entered samadhi-marana in 1942 CE at Isari in Bihar.
I remembered having read about him in the biography of Kshullak Ganesh Prasad Varni (1874-1961), but had not thought about him. Kshullak Ganesh Prasad Varni is regarded to be a pioneer in the Jain society, responsible for an awakening, though study of ancient texts, establishement of schools.
It turns out that Baba Bhagirath Varni was a major inspiration to Kshullak Ganesh Prasad Varni. The Jain scholars of that generation, when India was still a slave nation, laid the foundation of the Jain institutions today.
Ganesh Prasad Varni was born in the Asati community  and Bhagirath Varni was born in the Jat community.
Today Kshullak Ganesh Prasad Varni is remembered for his autobiography "Meri Jivan Gatha", sections of which are sometimes quoted in Jain magazines. Prof. Ravindra K Jain in his "The universe as audience: metaphor and community among the Jains of North India" wrote a whole chapter using it.
The lectures of Ganesh Prasad Varni were recorded and then transcribed They are avaialble on the web. Unfortunately tape-recorders were not that common during earlier, and thus we don't have recordings of Baba Bhagirath Varni.
I am still looking for the written works of Baba Bhagirath Varni. I have seen references to some of his writings, but I think they need to searched in some of the libraries.
He was a senior friend of Ganesh Prasad Varni. It was Baba Bhagirath Varni who helped set Ganesh Prasad Varni on his path.
Kshullak Ganesh Prasad Varni writes about him:
"..Such a fearless tyagi are rare today. Since he became a bramhachari, he has not touched money. He had given up salt and sugar for life. .. Everyday he used to read Kartikanupreksha and Samayasara. .. His shastra-pravachana used to be very influential. The Syadvad-Vidyalaya was founded with his help and encouragement..."
Here is the story I have read in a book.
Both Bhagirath Varni and Ganesh Varni wanted to study nyaya (logic). They went to a famous Brahmin scholar Jivanath Shastri in Banaras, with two Jain nyaya texts - Prameya-Ratna-mala and Apta-Pariksha with them. They offered Rupee 1 as initial dakhina, and urged Shatriji to teach them from those books.
The Shastri, noting the texts belonged to the Jain tradition, became angry. He threw the dakshina and the books away and said: "I don't even touch such texts".
Stunned, the two returned to the dharmashala where they were staying. In the same dharmashala, a Lala Jhammanlal of Mathura was staying. Hearing their story, he donated them a rupee.
Then a postcard used to cost 1 paisa, and rupee was worth 64 paise. They purchased 64 postcards and sent them to potential donors urging support for establishing a Jain center of learning in Banaras.
Here is the rest of the story.
They received several positive replies, among them an offer from Babu Devkumar of Araah who offered them the use of the dharmashala of Bhadaini as a site.
They successfully established Syadvad-Vidyalaya at Banares which eventually became a major center of Jain learning, said to be comparable in impact to the Aligarh University for the Muslims. Baba Bhagirath Varni served as the initial "Superintendent" (that was the title used for the main administrator. Ganesh Prasad Varni want on to establish the institutions such as Sattark-Sudha-Tarangini at Sagar, where he served for several years.
 "Varni" means Brahmachari. It is incidentally also used for the founder for Swaminarayan Sampradaya who was known as Nilkanth Varni at one time. Kshullak means a junior monk. Kshullak Ganesh Prasad Varni has become a full monk just before his death.
 A trader community in Bundelkhand. It is counted as one of the communites with "Jain lagaar" i.e. with a "touch" of Jainism, in Vardhamana Purana of Navalsah Chanderia (1769 CE).