Unlike the Romantic Road, where I think the attraction is not the road, but the towns on the Road, on the Alpenstrasse, I think it is the road itself, and the scenic views from the road that make it interesting. From 2000 to 2013, I did most of the Alpenstrasse, although in pieces, not in one trip. all by public transportation.
Prior to 2007, I had made multiple trips between Sonthofen and Lindau. These were by rail, not on the road, although the rail line pretty much parallels the road route. I had also made separate bus trips from Sonthofen to Füssen following the Alpenstrasse.
In 2007, I went from Oberammergau to Wieskirche by bus. All but the access road down to Wieskirche from the Steingaden to Echelsbacherbrücke road is part of the Alpenstrasse. Then, in 2013, I went from Oberammergau to Garmisch-Partenkirchen, then to Bad Tölz, all by bus. Instead of doing the road loop south to Tegernsee, I went by train via Holzkirchen to Miesbach, then on to Bayrischzell, then over the hill to the Inn river and Brannenburg.
Earlier, I had followed the road from Inzell to Reit im Winkl to Frasdorf. I couldn't do Berchtesgaden to Inzell, because there is a section from Hintersee to Schneizlreuth with no bus service.
So I have done more or less the entire Alpenstratsse except for the section between Füssen and Wieskirche, between Bad Tölz and Miesbach, the section between Brannenburg and Frasdorf, and the section between Inzell and Berchtesgaden.
The most interesting legs, for me, were the part between Sonthofen and Oberjoch, up the switchbacks on the mountain face out of Hindelang, Pfronten, maybe, between Garmisch-Partenkirchen and Bad Tölz, along Walchensee and down the switchbacks into Kochelsee, the section over the ridge between Bayrischzell and Oberaudorf, through Tatzelwurm. If there is a town on the Alpenstrasse I would like to stop in and spend time, it is Reit im Winkl.