One of the private firms that the Education Department hired this year to help collect nearly $1 billion in unpaid federal student loans has asked Secretary Terrel H. Bell to use private attorneys to go to court against debtors.

Without the threat of litigation, explained William Inglehart of GC Services Corp., a debt collector is like "a soldier operating without a rifle."

The Justice Department is responsible for prosecuting those who refuse to repay their federal loans, but Inglehart contends the agency doesn't have the time or money to prosecute small debtors. "Some little guy who owes a $1,300 student loan is not a sexy matter to an attorney at Justice," he said.

The Education Department's drive to collect unpaid loans has not been as successful as Bell had predicted when it was launched in 1981. During a 1978 test project, private collectors reported a 10 percent recovery rate, but, so far, the firms have collected only 1.5 percent of the overdue loans they have gone after, a Bell spokesman said.

Under its contract, Inglehart's company gets 24.5 percent of the loan money it collects; the other contractor, Payco American, gets 38 percent. The rates are different because the firms are seeking different amounts of money in different regions.