HOw do you know the reason the assessment was assuming 1 bath? Did you speak with the appraiser? Since the crash appraisers have become much more conservative on values, there are always exceptions to this but it has certainly shifted. The strongest thing used in an appraisal is price/sq ft the differences from home to home are not as critical as what homes in your area are selling for per sq ft.
It should not change your property taxes, each municipality in the country can vary slightly on how they handle tax assessments but in my experience a tax assessment change is not triggered from a refi or appraisal. Most common things to trigger a reassessment for taxes is the sale of the property or a county wide reassessment where all properties are adjusted (this is usually done every 5-7 years)