We report the first use of a ring cavity to both enhance the output power and dramatically narrow the linewidth (<1 MHz) of blue light generated by four-wave mixing in a rubidium vapor cell. We find that the high output power available in our cavity-free system leads to power broadening of the generated blue light linewidth. Our ring cavity removes this limitation, allowing high output power and narrow linewidth to be achieved concurrently. As the cavity blue light is widely tunable over the Rb855S1/2F=3→6P3/2 transition, this narrow linewidth light would be suitable for near-resonant rubidium studies including, for example, second-stage laser cooling.