Komoot has the itinerary as do the following sites, albeit in German.
https://www.radlland-bayern.de/routen/romantische-strasse/
https://www.adfc-radtourismus.de/romantische-strasse/
https://www.romantischestrasse.de/radeln-wandern-golfen/radfahren-gps-tracks (also in English)
You’ll find plenty of pension/B&B places or campsites (although German sites are quite pricey in my experience so I would wild camp, setting up a tent somewhere out of town after having eaten in the evening).
You can get a train from London to Munich, through the tunnel then either via Paris or Brussels. Takes around 10 hours either way. Brussels is probably easiest as you only need to change platform, whereas Paris you need to change station (it’s only a 10 minute walk, but with bike box etc not so easy).
Füssen to Munich is a days ride.
German trains generally have a section for bikes, excluding the intercity ICE trains. ICE you can take a bike if it’s boxed up.
The 49€ Germany wide ticket would be useful, but it excludes ICE trains.
You could train it to Munich with a bike box. Trains are around 200€. Dump the box in Munich and ride out train it to Füssen. Ride the Romantic Road and then follow the Main river downstream till you get to the Rhine and follow that to Rotterdam.
I road the Main from Bamberg to Rotterdam a few years ago on a fixie. It’s all more or less downhill. I wouldn’t do it again on a fixie, though.
