The credible interval gets larger the further you extrapolate from the data. In this case, the data density is approximately the same throughout, so that broadening is not observed, and the credible interval is dominated by the estimate of the assumed additive noise contaminating the observations ($\sigma_\mathrm{nois}$). If you extended the plot, say from -100 to +100, I suspect you would see the broadening.
The width of the band look about right for a 95% credible interval, it has about as many data points lying outside it as would be reasonably expected.
If you expect the noise depends on the attribute/feature, you need a heteroscedastic Gaussian process model.