Turn off the valves to the shower. Thawing a pipe with the water turned on increases the risk of a pipe rupture.
Place a space heater inside the bathroom to raise the temperature above freezing to remove any exterior ice. Plug in a hairdryer and aim it at any thicker ice to melt it at a faster rate.
Pour hot saltwater down the shower drain. The heat and the salt both help break up ice.
Run a heat gun over the frozen areas of piping to thaw out the ice inside of the pipe. Heat tape is another option as well. Wrap it around the pipe to remove the internal ice and then throw it away once you're finished.
Turn the water valves back on once the bathroom itself and the pipes have been sufficiently warmed.