Look it had been repeatedly said that there is and will be movement of people across the border of neighbouring country. It just natural. I wont be surprised if I bump into a Bangladeshi even in Myanmar. Even I can take you to BangaBazar the cheap cloth market and show you hundreds of Indians trading there. Other than BJP RSS and PDF version of 20 to 50 million, all other statistics (India govt) suggest more or less 300,000 Bangladeshis living in India. I feel it quite normal. Even 100,000 of Americans live in Mexico. What is the big deal? We housed more than 1/2 a million Burmese. We employed a million Indians. How many here complained about it? Infact we feel good, as somebody earning their Rizk here which is gifted by God. Nobody is taking away anything from us but its the opportunity which can be shared even with anybody if possible.
I agree with many of the things you said, and if general public had really such intention they could have informed the police. I could have. But it wont make any difference. The policeman will probably take some money from the poor guy, or beat him, why would anybody want that.
Also you will appreciate that illegal bangladeshis were not thought as liabilities but votebanks in India. But after security situation changed in late 90s, relation became bad with bd govt, there was support of terrorism from there, hence bangladeshis became liability and security threat.
Hence the need of building a fence(you may say it does not work, but the need is there)
I am not even talking about genuine local grievances(at state level) from bordering states which is a danger to federal structure of India.
Nobody in India can claim even a handful of pakistani being in India. Because there is no economic migration to India. Those who come are tracked and usually some action is taken.
We want bangladeshis respectfully deported to their home country, with all their money and belongings. I would even say GoI should give some monetary inducement for it.
For skilled workers, artists, poets, filmmakers, writers etc, our doors should remain open always.