Then why Bengal became a breakaway province of Mughal Empire. Starting from Nanda Empire to the partition of India, Bangladesh was always ruled from some Indian city, even Gaur is an Indian city.
I think, you have a wrong conception of ruling. It is not the Cities that rule a region or a country. Rather, it is a certain group of people who rule. In case of Bangladesh it is a new country, but the people are the descendants of those who fought Delhi for centuries during muslim period.
The last great war was fought for at least a 30 year period from (1575AD - 1605AD), although it really started in 1526AD after Babar won the 1st Battle of Panipath and captured Delhi. All the Pathan retinues and dependents of (killed) Sultan Ibrahim Lodi vacated north India and came to take shelter under Sultan Nasrat Shah of an independent Bengal.
It was Sher Shah who finally took over the throne of Bengal from Sultan Mahmud Shah in 1537 and joined this region with Delhi Sultanat in 1539 after he defeated (Mughal) Humayun in two battles at Chousa and Bilgram. So, Bengal was not really a breakaway Province of Delhi, although we all cherish the good governance of the Mughals.
The Pathan retinues and dependents again fled Delhi and west/north India after Adil Shah was defeated by Humayun at the 2nd Battle of Panipath in 1556AD and fled to Bengal to take shelter among their own kin and relatives. These people spearheaded the long 30 year old war against Delhi. All the Muslim Chieftains (Baro Bhuyan) of Bengal of that time who fought against Mughal domination belonged to this stock.
Same as we cherish Mughal time we also cherish the time of Sher Shah because he was from Bengal region. His grandfather was from Afghanistan, but his father and himself were born and brought up in Sasaram of today's Bihar, which, in historical times, was a part of greater Bengal. There are many millions of such foreign-blooded Muslims in Bihar, west Bengal, Orissa and Bangladesh.
Yes, Pataliputra was the center of a great empire that extended up to Afghanistan. But, this history cannot be analogous to the history of Bengal that unraveled after the conquest of this region by the Muslims from Afghanistan under Bakhtiar Khilji in 1198AD.
As I said not Cities but the people rule. So, it is equivocal to cite the name of a few cities that lie in today's India. These are Lakkhanabati or Lukhnouti, Gour, Pandua and Murshidabad.