I understand how to relate bin numbers of FFT output to frequency when dealing with a uniform FFT. How does this process work with a non-uniform FFT?
The magic of NUFFT is that you create a (oversampled) grid of equally spaced points by performing the interpolation and convolution of your unevenly spaced data. This is mostly done by using Gaussians. After that you apply the Fast Fourier Transform and minimise the effects of the filter you applied previously. Although this method was described by Dutt & Rokhlin in 1993. Currently you can find other, like ones based on Multiresolutional Analysis and Least Square Interpolation.
Nevertheless, you always end up with evenly spaced frequency bins - there are no unevenly spaced frequency bins due to jitter in the time domain.
If you wish to dig into math, then please refer to (among many others):