The bidirectional broadcast channel denotes a broadcast channel with two receivers where each receiver knows the message intended for the other. We consider streaming sources where messages of each user arrive as bit-stream to the encoder. Thus our main quantity of interest is the bit error probability. By extending Sahai's argument to bidirectional broadcast channel, we show that under maximum-likelihood decoding the bit error probability decays exponentially in delay with positive exponent for all the rate pairs inside the capacity region. We also show existence of deterministic codes which achieve exponentially decaying bit error probability with delay.