The noise generator has a programmable bandwidth (which I'm trying to confirm) so maybe I could pass the signal through a highpass filter, then a good RMS voltmeter. I could plot voltage as the noise bandwidth is varied, and estimate the 3 dB frequency. That would avoid finding room to store another boatanchor.
Or we could use a long-record scope, export the waveform data, and FFT that. Heck, LT Spice could import the waveform and FFT it, or play other games. Build my own wave analyzer!
(Or just trust the math, and not actually measure the noise bandwidth.)