Vinegar in the water helps remove soap. On a warm to hot day, fill a large pail with very warm water and add vinegar. Take it outside, along with a towel for drying. Simply put her in to rinse. Since you're only rinsing and not doing a full wash, the water should maintain the necessary heat to keep her from being chilled. Make sure to keep her head well above the water. If necessary, use your hand or a small cup to pour water on her head/shoulders.
Run your fingers through her feathers, particularly in the areas you feel were not well rinsed, being careful to not damage feathers. Take her out of the pail and let her drip dry for a bit, then wrap her in the towel to remove as much moisture as possible.
If the feathers are truly being damaged, pluck them. It will take about 6 weeks for a new feather to grow in completely.