An out-of-the box idea, but I am not able to envision any scenario that would allow this to pencil out. It is difficult enough to have our current roads repaired and maintained, and there is a steady supply of excise taxes. The cost for such an endeavor - land acquisition, legal, construction, maintenance, interest costs on the bonds (a risky venture would require a high interest rate), along with the cash flow that would be required for a bond sinking fund to ensure the bonds could be repaid, would likely overwhelm any expected revenues that could be generated.
Imagine the land acquisition costs alone. One 20 mile "bike road" a mere 8' wide would require 844,800 sq. feet, or 19.4 acres. In reality, you would probably want something at least twice as wide. How would the land be acquired? Eminent domain? If so, that could raise a host of legal and political issues and add to the acquisition cost. Even when a right of way in donated by, say, a railroad for use as a trail, development and construction can be a costly and lengthy affair.
Of course, there and some bike trails that see enough useage that they generate commercial benefits to existing business and in some cases actually result in new businesses. But I seriously doubt that model would work in most (or even many) places. Seasonality is one reason. Such roads in many parts of the country would be sparingly used, if at all, for many months out of the year due to weather conditions. Population density is another reason.