Buying at the other end seems difficult regarding the registration, and in these countries RTW-worthy bikes are all imported, so just as expensive as where you're coming from.
I'm in Thailand now and I can't say it's worth coming here given that you have to airfreight over Myanmar. (I'm coming from Japan and had to use Bangkok as a midpoint due to outrageous airshipping rates from Japan.) Nice place (and I'm sure it's the same for Laos and Cambodia), but not especially so for bikes.
In short, I'd buy a bike and register in your own country, and ship it to Bangladesh. That way the bike rego has your name and address, it's from the same country as your passport, which makes it much easier for FIA to issue you a Carnet de Passage Douanes and make it much easier for customs officials in each country to believe you.
I specify Bangladesh because I've read in other forum posts that the customs there are better than India. Remember that customs officials at airports are significantly better than those at surface freight terminals, I'd value that at being worth $1,000 USD by itself.