Shodan Enterprise includes bulk access to all the data that Shodan collects for the purpose of having your own, on-premise copy of the Shodan database. This document outlines the currently-available datasets, methods to access the them and basic guidance on working with the bulk data.
To learn more about the data itself, specifically banner data, please check out the Datapedia. It is our reference document that outlines the properties that can exist on a banner, provides a JSON schema, sample data as well as search queries to identify services that contain the property. For example, this is how the screenshot data and accompanying OCR results are stored: