>We have discussed the possibility of incentivizing riders to help redistribute bicycles, although the effectiveness of this has yet to be proven.
This is almost certainly because no-one has the data or analytics yet. Seems like a very interesting problem algorithmically.
Even small incentives can have dramatic effects – look at the number of under-employed who recycle aluminum cans for 5-10¢/pop. It's by far the most cost-effective way to increase the rate of recycling. There are certainly quite a number of people willing to move bicycles a couple miles for $1-2. I know I'm beating the HN dead horse here, but markets do tend to be efficient at allocating resources when the basic costs are set correctly.
With your mobile app, you have the advantage that you know not only where a bike was picked up, but how far the customer had to travel to reach it. With so much data at your disposal, you should be able to get a pretty good predictive handle on the ebb and flow of demand in the system.
It'll be cool when I can subscribe to a higher tier to have my demand weighted more heavily. ;)