You can easily enable this option when customizing the output settings of your batch prediction. If you are using the BigML Dashboard, click the highlighted icon under the Configure panel and provide a name for the confidence column before you click the Predict button.
Note: although the option is called "confidence", for regression models, it includes the prediction expected error.
If you are using the BigML API, you need to set as "true" the "confidence" parameter, and provide a name for the confidence column with the "confidence_name" parameter. Click here for more details.