Thanks all!

I have read "World made by Hand" and also the "Dies the Fire" series (by S.M. Stirling.)
As I recall, in Kunstler's (excuse me, but VERY sexist) novels, people mainly used horses and boats for transport, though I'll probably steal some ideas from him.
In "Dies the Fire," Stirling got around the problem by having a whole lot of very handy people being the survivors ("Oh, I just happen to be a bowyer and a blacksmith! And you're an herbalist/doctor/veterinarian? - how convenient!) They did use bikes but I don't think he addressed the tire issue.

I have read about wooden tires being used, but as the roads fall apart I think this would become more and more difficult. (Though the people in the story do work to maintain major routes.) Boneshakers sound about right! I have considered some sort of sap/leather/wood combination but don't know if it would be feasible. I might have to take out the bikes...though my main character (as of now) works repairing and rebuilding bicycles. I could give her a different trade.

My story is not aimed at a particular audience, but I think the finished book will fall into the YA category. Believing as I do in the innate goodness of the great majority of people, it describes more of a utopian than a dystopian future. Most of the events in the novel take place about 50 years after the End Times, in what is something like a transition town/permaculture society. There are still books and some clothes, but anything that would be likely to spoil, break down, or rot has done so (medicines, canned goods, solar panels...bicycle tires....)

There is no single cataclysmic event that brings about the apocalypse; there is increased flooding and decreased snowpack (drought), violent storms and fires that overwhelm the ability of the government to maintain the infrastructure, an economic collapse brought about by various factors, rampant viruses and famine, and a complete breakdown of the electrical grid, all of which happen over the course of about 20 years.

Most of the people I know do not have horses, antique weapons collections, water or wind mills, wells with hand pumps, nor the kinds of skills needed to make, maintain, or do things by hand. From what I see, most people (including me) would cling to the past as long as possible rather than accept that industrial civilization is over - thus leaving the next generation in the lurch.

The survival literature I've read for research mainly focuses on the short term (food storage and the like) or wilderness-type survival.

I'd like to avoid the inconsistencies I read in so many futuristic novels.