Did a lot of riding whilst I was out there for a couple of months (took my Anthem with me) but only actually did a couple of days of proper riding with another guy from the UK.
Got hold of a walking map and followed some of those trails, no issues with walkers other than I think they thought we were nuts, even got cheered on a few times!
Japanese walking maps show the time to complete a trail, so if its short and has a high number avoid! It did get interesting at one point when we went flying over a crest to find a set of stairs the other side!
I was staying in a place called Aiko-Ishida and went into the mountains nearby in Isehara.
If you only have a couple of days and need a bike then an organised trip is probably a better idea. They can be funny about taking bikes on trains, you generally need to have it in a bag or similar, it’s quite rare that you can just wheel it on like in the UK.