Well get out your books and reference the devices... a constant current diode is a jfet operated at it's "pinchoff voltage"... they are available in 2 lead diode like packages... a constant voltage power supply feeding the diode will produce a constant set of conditions that the thermistor can react to.
The Wheatstone Bridge is a fine tool but because of it's bi-polar nature is much more difficult to directly interface to the A/D inputs on the Arduino.
Reference the "Star" method of power supply distribution in your texts and see what I was talking about as far as noise both distributed from the power supply and created by individual elements...
Getting back to the thermistor issue, a constant current through the thermistor will produce a variable voltage, temperature dependent and that will give you the information you need from a stable source.
I hope this helps a little. Unfortunately I need to go and do some "Honey Doo's" now and I will be busy for the next 3 or 4 hours... I think.
Doc