The answer to this is pretty large in scope and current understandings of the word "international" may not always hold good.

Firstly regarding WW2 Bengal, any foreigners apart from the British who were the ruling power would probably be present because of the war. There was a pretty intense conflict going on with the Japanese in Burma and there would be extensive allied military presence because of that.

Now, to tackle this chronologically Alexander's invasion is the first "big" foreign incursion. Now while he left pretty soon, his invasion opened the doors to Indo-Grecian contact. Alexander's general Seleucus who took over the Persian part of the empire has an envoy Megasthenes at the court of Chandragupta Maurya, the Maurya emperor. During this time, from Kautilya's Arthasastra, an immensely authoritative work on political economy we come to know that the municipal administration of the capital Pataliputra had a committee dedicated entirely to taking care of foreign visitors.

Moving on, Chandragupta's grandson Asoka started a new policy of religious welfare and paternalism based on Buddhism and sent out missionaries to many places including China, Ceylon (Sri Lanka) the Middle East and even Greece. So it might be fair to conclude that foreign interaction was pretty high during this time.

The north-western part of India came under pretty heavy Greek influence especially from the Bactrian Greeks. The Gandhara school of art is a clear testimony to the influence of Greek style.

The Kushana empire of Kanishka extended from Central Asia to North India. Central Asian influences were pretty clear here. The ensuing Gupta empire had flourishing trade relations with Rome. Essentially when you get rich and powerful empires and foreign trade a foreign trade community is pretty much guaranteed.

Even when the empires fragmented into smaller states like in the time of Harshavardhana there was foreign contact and interaction as testified by the accounts of the Chinese traveller Hiuen Tsang. A useful footnote here is the Nalanda University in modern Bihar which was an ancient seat of learning and had a number of foreign students.

With the Muslim conquest under the Delhi Sultanate and the Mughal Empire India had extensive cultural and commercial contact with Afghanistan, Persia and Central Asia. Many foreign adventurers, warriors, philosophers and merchants came and settled in India at this time. Perhaps the best example is the Empress Nur Jahan, wife of the Mughal Emperor Jahangir. Her father was from Central Asia, in modern terms she would probably be a first generation immigrant and yet her intelligence and political ability saw her become a significant force at court.

With European contact we have European enclaves - Portuguese, French and even Danish. It is interesting to note that prior to English domination Bengal was host to a powerful and rich faction of Armenian traders and merchants.

In fact the period of British rule saw a lot of foreign influence cut away as the British were extremely paranoid about foreign entry. In the beginning of the 19th Century even British people not supported by the East India Company were restricted from entering.

Modern India is my area of research and I can assure you that even in the 1920s the British routinely restricted foreign entry, American and German Visa applications were rejected. I have seen the files.

It should be noted though that even in this atmosphere the Nobel Laureate Rabindranath Tagore invited Japanese and German scholars to his University at Santiniketan for cultural exchange.

Well there you have it. Its not very thorough, mostly because I wrote the entire thing from memory after a very tiring day.