To use this feature, click on the directions icon and select a starting point and a destination with any points in between that you would like to add. Next select the biking directions icon and a panel on the left side of the map will show distance, estimated travel time, route options and the elevation profile for each route. In the elevation profile panel there is an option to hide or show bike paths. To switch between routes, click on the desired route on the map or on the elevation profile panel. You won't see an elevation profile for routes that are essentially flat.
This new elevation profile feature is only available at the moment for desktop Google Maps and not any of their mobile Google Maps apps. Hopefully Google will add it for mobile use in the future.