BART spokesman Jim Allison declined to go into detail about how close the two sides were to reaching an agreement and averting a second commute-crippling strike in less than three months.
The unions have vowed to walk off the job if no new labor agreement is reached by Monday. A strike would force hundreds of thousands of commuters who use the nation's fifth-largest rail system to find other ways to work.
BART workers went on strike for nearly five days in July before Gov. Jerry Brown mandated a cooling-off period that ended Friday.
Saturday's bargaining session was supposed to begin at 9:30 a.m. after 12 hours of negotiation Friday, but the two sides agreed to delay talks so each side could meet privately Saturday morning.
BART spokeswoman Alicia Trost said BART General Manager Grace Crunican planned to attend the talks for the second day. The unions said Crunican's presence had made a difference after they had repeatedly criticized her for not being more involved.
Trost said BART was preparing to offer riders free trips from the East Bay to San Francisco on buses if a strike occurs. She also said a dozen managers have been certified to operate BART trains, but the transit agency isn't planning to use them immediately. She said the BART board of directors would have to approve the use of managers as train operators.
"The board would need to decide if they want BART to operate limited train service by managers," Trost said. "That isn't the plan right now."
Amalgamated Transit Union Local 1555 and Service Employees International Union local 1021 want a raise of nearly 12 percent over three years, while BART has proposed a 10 percent increase over four years. BART said workers from the two unions now average about $71,000 in base salary and $11,000 in overtime annually.