Since $2^{a}=5^{b}=10$, we can write $a=\frac{1}{\log_{10}2}$ and $b=\frac{1}{\log_{10}5}$.

Then,
$$\begin{align} \frac{1}{a}+\frac{1}{b} &= \log_{10}2 + \log_{10}5 \\ &= \log_{10}(2 \times 5) &&\text{(Using the product rule for logarithms)} \\ &= \log_{10}(10) \\ &= 1 \end{align}$$

Therefore, the correct answer is $\boxed{(B)\ 1}$.

This problem involves converting exponential equations to logarithmic form and applying the properties of logarithms. It is a basic question that tests one's understanding of these concepts.