There's a fair range of vintage bikes out there waiting to be done up - Minsks are fairly easy to find, there's usually a few advertized on this site, and the Minsk club may know about other places to look for other vintage bikes.
If that's not what your after there's a lot of others like Simpsons or Uwas which don't tend to be found in expat circles and usually in the countryside owned by poor farmers. The best advice I could suggest is to get a Vietnamese mate to go through some Vietnamese classifieds for you and have a look what's out there. It'll be more difficult than rocking up to a shop, but you never know what gems you might find.

What kind of bicycle you want?

We just import old bicycles from Japan (not China) in Haiphong seaport. Some shops in Hanoi sell them but I think you better go to Haiphong.

I haven't seen any shop sells old American/European bicycles in Hanoi.

i guess the most important factors are that the bike is made of rigid steel, like 531 reynolds, and has a straight top bar. a japanese fuji,miyata or panasonic would be fine, but also peugeot, schwinn, or raleigh, would be okay too.

cheers

Ah, I see what type of bicycle you want. I used to have a Japanese sport bicycle (it looks like bicycles they ride in Tour de France). Unfortunately, I've sold it.

You said you've tried Ba Trieu so I suggest you take a trip to Hai Phong. No guarantee you can find what you want there but the price is cheaper. In addition, there are more types of bicycles so it's easier for you to choose than in Hanoi.

Goodluck.