We revisit the classic basic counting problem in the distributed streaming model that was studied by Gibbons and Tirthapura (GT). In the solution for maintaining an $(ε,δ)$-estimate, as what GT's method does, we make the following new contributions: (1) For a bit stream of size $n$, where each bit has a probability at least $γ$ to be 1, we exponentially reduced the average total processing time from GT's $Θ(n \log(1/δ))$ to $O((1/(γε^2))(\log^2 n) \log(1/δ))$, thus providing the first sublinear-time streaming algorithm for this problem. (2) In addition to an overall much faster processing speed, our method provides a new tradeoff that a lower accuracy demand (a larger value for $ε$) promises a faster processing speed, whereas GT's processing speed is $Θ(n \log(1/δ))$ in any case and for any $ε$. (3) The worst-case total time cost of our method matches GT's $Θ(n\log(1/δ))$, which is necessary but rarely occurs in our method. (4) The space usage overhead in our method is a lower order term compared with GT's space usage and occurs only $O(\log n)$ times during the stream processing and is too negligible to be detected by the operating system in practice. We further validate these solid theoretical results with experiments on both real-world and synthetic data, showing that our method is faster than GT's by a factor of several to several thousands depending on the stream size and accuracy demands, without any detectable space usage overhead. Our method is based on a faster sampling technique that we design for boosting GT's method and we believe this technique can be of other interest.