Do things play out that way though? Every time you raise prices, fewer people use it, resulting in requiring another price increase. Demand for public transit is actually pretty price-sensitive. Look at what's currently going on with the New York subway system, for instance.

Now, consider the case where the current prices could actually cover costs if utilization was high enough. (I don't know if that's true for BART, but it's certainly possible for a public transit system.) Wouldn't it make much more sense to increase ridership than prices?

This strategy is hardly unique to publicly-funded projects. Lots of businesses sell a new product at a loss, expecting to grow their sales of it until they can use economies of scale to make the product profitable.

A policy of naively basing prices solely on recent demand and current costs misses a lot of possibilities. It's very worth considering how increased demand changes economies and pricing with a long-term plan in mind.