"But I won't get emotionally involved yet. There have been so many ups and downs. One woman tricked me and her own daughter into believing we were related. I need to see the tests," he says.
His caution is understandable. After a spate of claims by fake Amerasians, the US consulate has tightened its visa application policy for people claiming US parentage.
Even Hien's son turned out not to have been Bill's child, according to two recent DNA tests.
"More and more American men and Amerasian children are trying to find each other," said Phan, a Vietnamese man who works as a liaison between the two groups.
"But it's very difficult. In most cases the mothers remember nothing. Many were cleaners in US bases or prostitutes, who were not well educated and had several boyfriends at the same time. After the communists took control in 1975, many mothers were afraid of being associated with the enemy so they burned all evidence of their old lovers," he says.
That has not stopped some veterans from launching what appear to be hopeless searches. Last month Rafael Pagan, a former army quartermaster, returned to Long Binh army base to look for a girlfriend he had last seen in 1969.
"I loved her and she was pregnant when I left so I still feel responsible to help my child," said the 60-year-old, who now works as a store clerk in a New York hospital.
"The problem is I don't remember her name," he says.
Despite the lack of information, several Amerasians have replied to an ad he put in the newspaper with his picture and details. Two have sent off DNA samples, each of which will cost several hundred dollars to be processed.
Pagan says he is not daunted by the cost or the long odds.
"I went to Saigon in the hope that I'll see some results. Whatever it takes, I will do it," he said.
Vietnam's most famous Amerasian is Phuong Thao, a pop singer who was conceived the night before her father was posted back to the US in 1967.
"Mum never talked about my father. I never asked. She thought it was impossible to find him. She just wanted to forget," Thao says.
"But I thought about him. At school, I was taught that Americans killed many Vietnamese. So I wondered whether my daddy was a good guy or a bad guy," he says.
When she was 28 years old she got the chance to ask the question in person after an American writer helped her to track down her father, James Yoder, who had been unaware of her existence.
"The first time I met him, I cried like a baby," Thao says. "I looked exactly like him."
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