If you wish to study travel by public transit (meaning, the analysis models travelers actually riding the transit, not simply determining whether there is a close-by bus stop), then you need to incorporate the public transit schedule data into the network dataset you will use for the analysis. This documentation shows how you can do that in ArcGIS Pro: Network analysis using public transit data—ArcGIS Pro | Documentation
You will need to obtain the GTFS public transit data from the transit authorities you want to include and build a network dataset that includes this as well as the street data. You can use the Streetmap Premium Custom Roads product to combine high quality Streetmap Premium data with the GTFS public transit data.
Unfortunately, there is no nationwide public transit data available, nor is there a single location where you can obtain GTFS datasets for all agencies. Not every agency provides GTFS data, and not all agency that creates GTFS data will make it publicly available for download. Each agency has different data licensing rules, etc. It makes things complicated.
Additionally, I don't think you'd want to include all the GTFS datasets for the nation into one network dataset anyway because you could start to run into memory issues. The schedule data has to be cached into memory when solving. A better solution would be to create separate network datasets for individual cities or metropolitan areas and broker the analysis so that, based on the location of the inputs, it chooses the correct network dataset for that analysis.
Sorry I don't have a simpler answer for you.
