Rinse the rice under running water. In a 5-½ quart slow cooker, place uncooked rice, chicken breast, onions, carrots, celery, garlic, bay leaf, chicken broth, water, italian seasoning, salt and pepper. Cover and cook on high for 4 hours or on low for 7-8 hours. Remove chicken from pot during the last 30 minutes of cooking. Allow to cool.
slightly then shred with two forks.
Add the chicken back to the slow cooker and continue cooking vegetables through. Melt butter in a small saucepan.
Add the flour and cook for one minute. Whisk the mixture slowly while adding the milk, whisking to remove all lumps and until sauce has thickened and become creamy.
Add the bechemel sauce to the slow cooker, stirring to combine. Adjust seasoning with salt and pepper. Let sit 5 minutes, soup will thicken as it stands.