AC losses in a high temperature superconducting (HTS) coil are experimentally evaluated. Double-pancake (DP) coils with turn-to-turn electrical insulations are wound using bundle conductors formed with two pieces of rare-earth-based coated conductors located face-to-face without insulation to improve thermal stability. Five DP coils are stacked and subsequently four copper plates are soldered between the adjacent DP coils to form a small-size HTS coil for AC loss measurements. The fabricated HTS coil is immersed in liquid nitrogen. Before measuring the AC losses, the contact resistances between the DP coils are observed in DC operations of the HTS coil at first. After that, the total losses including the Joule losses in the joints between the DP coils are measured by integrating the products of almost resistive components extracted from the terminal voltages in the HTS coil and applied transport currents observed using a pickup coil over a cycle under AC operations. Net AC losses in the two-ply bundle conductor windings are obtained by subtracting the Joule losses from the measured ones. In order to understand the mechanism of AC losses in the two-ply bundle conductor windings, the influences of current amplitudes and frequencies are investigated experimentally and theoretically.