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Best bet is Clickbd cellbazaar or lokton dot coms.
50K is not going to get you very much I am afraid to say. ( read a pile of junk )
It is possible to get up to 220cc ( paperwork is dodgy but seems to be quite common practice here )
Also before teh 150cc rule came in there were a few larger bikes and they crop up occasionally have seem 250cc Kawa KLX, Royal enfield 350 and Hoda CB 650 again older bikes.
Hysong 250cc on one of those sites recently and a good Hysong 125 dirt bike but price was 170 k Taka
I repeat 50k will be junk, Good luck Kiwi Sam, what part of NZ you come from

Hi Kim & Mika,

Thank you very much for all your advice. I've had a look at the websites you've suggested and you're right, the bikes all seem pretty low quality but with a rather high price! There's an Honda XL125 that I may look into but the prices are a bit of a shock compared to India. You don't know of a big, honest, second hand dealership you could recommend? I suppose I don't mind paying a little over the odds to someone if they can help me with the ownership papers too. I have a Bangladeshi friend and I plan to put the bike in his name but he's up in Dinajpur.

I'm from the North Shore of Auckland, New Zealand but have lived in London the last three year and now... Bangladesh!

Thanks again for your help, I may have some further questions for you soon haha.
-Sam

Welcome, it frustrates me as well, would love to get the concept cafe racer royal enfield if they ever start manufacture, but does not seem soon, and certainly not here. I regret not buying one  when I lived in Delhi.
I have a friend that owns Marine North at Tutikaka ( excuse spelling )
Most Honda XLs here are 185's if you can turn a spanner, easy to maintain, and give a good service to it might be a choice, 45-80 000 BDT better than the 125's.
You fish? Golf? tennis? HHH?

My budget were 80k to 125k for a nice 150 cc Yamaha black color bike but no luck. Too many stolen bike with fake paper. If I pay 250 k then I can get a brand new Yamaha with genuine papers. Because of the traffic I was planning to buy a bike just to go to the Gulshan club. Kim n mika i love fishing, play tennis and swimming. Sam there is a place call Bangla Motor check that place you may find some thing that you may like. Or just go for electric bike no paper work no registration. They are srround 65k.