How to tune bandwidth in machine learning kernel model?
As shown in wikipedia for KDE, a rule-of-thumb bandwidth estimator can be given if the underlying density for your data is Gaussian. This estimator is given by: $h = (\frac{4\hat{\sigma}}{3n})^{1/5}$, where $h$ is the bandwidth of your KDE estimation, $n$ the number of data and $\hat{\sigma}$ the estimation of the standard deviation of your sample.

If the underlying distribution for your data is not gaussian, you can still try with this bandwidth, but it might smooth everything too much. In that case, you should go for cross-validation with smaller bandwidths.