Appeal. You're not wasting anyone's time. The court is there because you pay taxes. Whether you did it or not is irrelevant. You are entitled to be there.

By showing up, being dressed properly, etc, and being very polite you can ask the judge to reduce the fine. Explain that you can't afford it. If you explain that you could afford the fine if the judge could set up a payment plan (he can't) the judge might believe that you really can't afford it and reduce it substantially. Additionally you can also offer/ask if the judge would be willing to let you take a safety class put on by the League of American Bicyclists instead of the fine. Come prepared with a set of class dates. I'd be willing to bet that you could walk away with no fine at all and no class.

If you want to be tricky, find out what the last possible date/time is to delay the hearing. Do so at that point. Often the PO won't get word and will show up to find the hearing has been moved. Then before the 2nd date do the same if you can (sometimes you can only postpone once). When you finally show up, the PO is less likely to be there.