While not Google maps - this can be achieved on Open Street Maps - eg. https://www.openstreetmap.org/relation/3574625#map=7/34.153/134.934 (It's a long road so this may take some time to load)
You can either do this by directly searching for the name of the road in the search bar, but you'll probably find it easier to right click on a section of the road. ...
Although Google Maps doesn't do offline public transportation downloading, OsmAnd might help you here. It uses Openstreetmap data. Depending on the region, Openstreetmap data may be better, equal, or worse than Google Transit data. On the plus side, if you notice errors, you can go and correct it yourself and others can benefit from your corrections — all ...
After quite a lot of searching and testing, this is not possible with Google Maps. Downloading offline maps doesn't download public transport directions.
You can either:
Take a screenshot of the directions (like you do now)
Look for another app that can do this
HereWeGo and Moovit both have off-line modes.
HereWeGo is a general-purpose navigation mapping tool and can download maps.
Moovit is public-transportation only, however, it doesn't always work for long-distance trips if they are across its regions.