I wouldn’t suggest literally credit card touring here as you will be SOL more often than not. Electronic payment is just starting to take hold, but its pretty fractured right now with about 100 different companies trying half-assed at it, with loads of different apps and CC are not excepted at most places. If you just meant buying everything as you go, not keeping a stock of food and what not on you, you’ll be fine. Rare is an area in that region that doesn’t have a convenience store within a 5km radius.
The eastern shore of Biwa, from Otsu on up till about Hikone Castle, is pretty miserable with traffic and rundown old towns, unless you really hug the shoreline. From Hikone, up around the north shore, it gets into some hills, but also some very long tunnels (luckily with elevated walking/biking platforms, but still really loud and lots of car exhaust), and then out of the tunnels its really quite nice. Quiet, save for the small town here and there and other cyclists/bikers. About half to 3/4 of the way on the southwest side, you start to hit more city, traffic, tour buses, etc. again.
Last year I took a group beercycling/brewery/pub hopping from Southern Osaka up through Minoh (pretty nice if you go all the way up into the mountains) and then over to Kyoto. The Minoh to Kyoto leg was half suck (high speed traffic), half farmland and quaint Japan. That really is the problem with riding anywhere around the old and current capitals (Kyoto, Nara, Nagoya, Tokyo). The sprawling development and blight really doesn’t stop till you hit uninhabitable mountains or ocean, and there are few surface roads between. What might look like a 2-lane back road on a map could be packed with trucks and heavy traffic.
^^^^^ Wakayama loop would be pretty sweet. I can also suggest heading across the inland sea from Osaka or Kobe and ride around Shikoku. There is actually a proper bike route that island hops over there and a lot of bike-centric hotels and what not.
You can basically take your bike on any train, any time. Just stick to the back or front and make sure its at least front wheel off and wrapped. Some train station workers don’t care as long as dirty parts are covered, but others will get in your ass about something like a seat sticking out. I’ve used a “rinkobukuro” to take various bikes across the country on cheap train tickets and the bullet trains. Never had an issue.