A household model is formulated to facilitate careful development and performance testing of bid-based transactive energy system (TES) designs with voluntary customer participation. The optimal general bid-function form for households with thermostatically controlled loads is derived from dynamic programming principles, based solely on general household thermal dynamic and welfare attributes. Quantitative forms are determined for these optimal bid functions, given quantitative forms for these attributes. These quantitative attributes are used to construct representative household types based on clusterings of correlated parameter values. Bid comparison, peak-load reduction, and load-matching test cases conducted for a 123-bus distribution system operating under a generic bid-based TES design illustrate the usefulness of our methods for ensuring TES designs are aligned with local customer goals and constraints.