I've spent more than 4 month cumulatively traveling in the Black Forest, Bavaria, and the Tirol, entirely by public transportation.. The major sites are tied together by rail; getting to smaller areas might require a bus, but the buses were comfortable, modern coaches.
Black Forest: The Schwarzwald is basically served by a single north-south rail line running down the middle of the area, but it links major venues like Freudenstadt, Hausach (Open-air museum), and Triberg, plus some lateral rail lines to Stuttgart, Karlsruhe, Baden-Baden, Offenburg, Freiburg, and Bodensee. There is also an extensive network of buses to lesser places. If you stay in the Forest itself, you'll get a Konus Karte pass that gives you cost-less access to all of the trains and buses.
Romantic Road: The Road itself is not the attraction.. It's just an ordinary country road with lots of automobile, bus, truck, and farm equipment traffic. It's the towns themselves that are the attraction, and most of the significant ones are tied together by rail. There are a couple of stretches, namely Füssen to Landsberg and Nördlingen to Weikersheim where the only access (except to Rothenburg) is by bus, but I've traveled both of those stretches without difficulty. The only major venue not accessible by train is Dinkelsbühl, and it is a 40-45 minute bus ride from Nördlingen.
Bavaria: The train lines in Bavaria mostly radiate out from Munich, but there are some cross-links in the foothills of the Alps, like the Außerfernbahn through the Tirol and the Bayerische Oberlandbahn in the Tegernsee-Schliersee region. The region south of Munich is well connected by an extensive network of buses run by the Regionalverkehr Oberbayern (RVO).
There is a rail line running over Brenner Pass from Innsburck to Verona. I've only been on it as far south as Fortezza, but a few years ago I was planning on visiting the Dolomite area. There were buses from Brixen and Bolzen to Val Gardena. I imagine you would find them to Val di Funes as well.
