Prediction interval for general non-linear regression
Bootstrapping (which I think you are referring to as bagging, a specific algorithm that incorporates bootstrapping) is your friend here.

Simply train N models using N datasets, where these N datasets are created by sampling from your original dataset with replacement. Using these N different models, generate N predictions on an observation of interest. 

You can now use any sort of method to derive the confidence interval of interest with these N predictions, whether that is using a normality assumption, empirical percentiles (simple bootstrapping), etc.

The one drawback I see with this method is that if you have many observations to predict, this will quickly become computationally expensive. That being said, bootstrapping is easily made parallel.