I haven't used DCs but I use CitiBike in NYC all the time and it's the exact opposite of what PSU points out. The majority of riders are commuters, they're having trouble attracting tourists/day riders because they are unfamiliar. Hopefully with more and more cities getting bike share, that will change.
In regards to the bike, those DC ones sound like the ones NYC uses and they're designed to be big and bulky and clunky. You are not supposed to be speeding through pedestrians and traffic as fast as you can pedal, but because people will, they limit the gears and make you work triple time if you really want speed. The fact that they don't want them stolen constantly also play into that undesirable design. It's a mode of transit for a limited time. Nothing more, and it shouldn't be.
I love this idea, but the reality is that this can't even be considered bike share, it's for guests of the Hyatt. And being that most visitors to Jax aren't used to humidity, I'd imagine it won't be highly successful for the hotel. The real success will be showing the city it is an option, one they can't deny when they see with their own eyes these brightly colored bikes riding down the road.
I support bike share, but being that Jacksonville is more of a "suburban" city, I think they'll have an uphill battle against the suburban mindset of bikes are bad, road-hogging, nuisances.