The nanohertz frequency band explored by pulsar timing arrays provides a unique discovery space for gravitational wave signals. In addition to signals from anticipated sources, such as those from supermassive black hole binaries, some previously unimagined sources may emit gravitational wave bursts with unknown morphology in the nanohertz frequency band. To find these potential sources we model the signal with a collection of sine-Gaussian wavelets, where the number of wavelets used is searched over using trans-dimensional MCMC techniques. We similarly model noise transients that may occur in individual pulsars. The Bayes factor between these two models will determine if we detected a gravitational wave burst.