Sorry, SLA, you are wrong. I did the entire Romanic Road by public transportation in October, 2007.
OK, you can do it somehow if you have lots of time and are willing to accept unpleasant detours. But while public transport in the southern segment from Füssen to Nördlingen is unproblematic it's getting poor between Nördlingen and Dinkelsbühl and between Dinkelsbühl and Rothenburg, and it's almost inexistent between Rothenburg and Weikersheim / Bad Mergentheim. The Nördlingen - Dinkelsbühl leg is served by four direct buses a day, two of them transporting hords of noisy school children. Going from Dinkelsbühl to Rothenburg, a distance of 40km or 25 min. by car, in most cases implies a big detour by bus and train via Ansbach and Steinach - approx 90km in 2:11 and bypassing the delightful baroque castle of Schillingsfürst. Getting from Rothenburg to Weikersheim means almost always (with two exceptions a day) leaving the lovely Tauber valley - the only leg of the »Romantic Road« where it is really romantic - and doing a big and time consuming detour either by train via Würzburg or by bus and train via Schrozberg on the Crailsheim - Würzburg / Aschaffenburg line.
So, as a rule the average traveller will not be able to follow the RR by public transport on its northern leg. Mostly he will have to leave out Dinkelsbühl, Schillingsfürst, Creglingen (where he will miss the best preserved work by Tilman Rimenschneider, much better than the main altar of St Jacob's in Rothenburg) and often Weikersheim / Mergentheim as well.
That's a very annoying situation. It's partly due to the fact that the northern leg of the RR meanders between Bavaria and Baden-Württemberg, i.e. between the area of responsibility of two different transport authorities, and partly to the fact that, understandably, the VGN has no inclination to take over traffic that should be taken care for by the DB, which after the closure of the Nördlingen - Dombühl - Rothenburg rail lines simply has refused to provide an adequate replacement by buses. The Dombühl - Dinkelsbühl line will be reactivated in the near future, but according to the BEG (Bayerische Eisenbahngesellschaft) there are no prospects for the Nördlingen - Dinkelsbühl leg.