With how things are right now, you are correct that the West has the tools to spread democracy in Bangladesh. However, there is no vested interest for the West to pursue such a goal, remember the US don't interact with countries for their brown eyes sakes, there has to be vested interests and gains need to be greater than costs. Investment in Bangladesh's stability and economy will not turn to gains in a short amount of time, because it has lingered in undevelopment for such a long time, therefore i don't see any reason why the US would focus largely in Bangladesh.
Currently, i am pretty sure the Turkish government closely follows the developments in Bangladesh as they do in Pakistan, AKP always voices that the grievances of Pakistan and Bangladesh is our responsibility as well and we will do whatever in our power to help. But currently we don't posess same amount of power and leverage as the US does. BUT in few decades when the combined GDP of Malaysia+Turkey+Indonesia exceeds 15 trillion USD our combined leverage and influence will greatly grow. That is not to say these three countries should ignore the developments in Bangladesh for now, on the contrary the soil needs to be sown now, or Bangladesh will keep lingering in political instability.
Turkey is strong, but currently not strong enough. We have as a former empire a great concern for Sunnis worldover and a feeling of responsibility for their development. If we will be able to rid our country of foreign backed groups like PKK and ISIS, i am 100% confident the things you emphasize will take place because great minds converge, even without the need of communication - the stand alone complex
