In London we have a 'fare hopper' system for the busses. £1.50 and you can take as many trips as you like within an hour. Or you could stay on the bus for the entire day (if you really wanted too) and just go round and round and it would only cost you the initial £1.50.
So the cost doesn't scale with your journey time/length, and if you're popping to the shops or somewhere nearish you can often make the return trip within the hour and you only get charged the first £1.50.
Very rarely is the distance travelled short enough that £1.50 feels like an over charge or lack of value.
I guess my point is, £1.50 isn't quite free - but it is low enough that it encourages use of busses. Once the initial fee is paid, within an hour any extra trips are free. It works brilliantly.
The issue of 'how do you discourage short trips' is a non-issue based on my experience of how the busses work in London, imo. It would be an interesting case study to put infront of those who think regulating demand is the blocker here.