Edgar Davids' side drew 0-0 with Cheltenham last time out and they once again failed to score in front of their home fans, a task which was not helped when substitute De Silva was sent-off with three minutes left for a high challenge on Luke Wilkinson.
In a tight first half Jake Hyde headed a Mark Byrne cross wide before Wilkinson was just as wayward with a shot in the 35th minute for the visitors.
Hyde wasted another chance as he fired over just before the break, and five minutes after the restart the Bees striker pounced on some confusion in the Daggers defence but his shot lacked any power.
Barnet had Graham Stack to thank in the 70th minute when the goalkeeper tipped Medy Elito's thunderbolt onto the bar.
But after that the game limped to a stalemate, De Silva seeing a straight red for his challenge on Wilkinson just ten minutes after coming on.