If Bangladesh becomes uninhabitable those 150 million or so people will need to move. Four thousand years ago there weren't anywhere near that number of people in the area that is now called Bangladesh. The scale has drastically changed.
It's easier for an individual to move now than in the past. This is clear. But if an entire high population region becomes uninhabitable in a short period of time then it's difficult for that population to shift. The neighboring countries generally won't want to accept the incoming people and often times can't sustain the incoming population.
Look at the problems with a few million people suddenly going to Europe has caused. Imagine if it were 150 million people trying to get into Europe.
