Keep an eye out for announcements here (usually on Thursday or Friday) of the weekend's "Half-Fast" rides. Their distance and hilliness are briefly described, so you can choose among them for something that sounds about right.
You probably already know this, but if not: bikes need to be wrapped and at least partly disassembled in order to be carried on the train. If you don't have such a "bike bag", then what you need is called in Japanese rinkōbukuro. These needn't cost much and are easy to find. If your bike is large by Japanese standards, don't assume that any bag will fit it. Every now and again there's an announcement here of bike bags that will take unusually large bikes, or that are particularly good value or particularly light. The shop GS Astuto (here) is selling these, which sound good.
And GS Astuto is also the place for tuning up your wheels. (The boss may be away in Europe right now, but business carries on.)