Generating band-limited NRZ signal
The first concept that I think will be helpful to see is pulse shapes that repeat in time at consistent rates. If you repeat a fundamental pulse shape in time, the result in frequency will have the envelope of the Fourier Transform for that pulse but will only contain frequency components at multiples of the repetition rate (harmonics).  Thus the Fourier Transform becomes sampled in frequency at multiples of the repetition rate in time. For example see the cases below for NRZ signals with different duty cycles, knowing that the Fourier Transform of a square pulse is a Sinc function in frequency with the first null at $1/T$ where T is the width of the pulse.





Now consider what occurs if the NRZ data has a pulse width of 0.05 seconds like the first example but is a random pattern 101101110001... that doesn't repeat for 10 seconds - the envelope will still be the same as the first example with the first null at 20 Hz, but the harmonics will appear every 0.1 Hz, the spectrum will appear continuous. Extend this thought to random data that never repeats and the spectrum will indeed be continuous with the same shape. 

So to answer your question the bandwidth of an NRZ pulse is infinite, but the bandwidth of any time limited pulse will be infinite if you review the Fourier Transform equations. However for practical considerations we can define bandwidth to be % of power within a certain frequency band, or ignoring spectral content that gets below a certain insignificant value.

With that in mind, the bandwidth of a Sinc pulse in frequency (NRZ signal in time) is still quite large, since the peaks of the Sinc only roll-off at rate f in frequency (or 20 dB/decade).  By shaping the pulse edges in time (slowing the transition rate), we can significantly limit the bandwidth.

A common approach is to reverse the case of the NRZ signal above, and use time-limited versions of the Sinc function in time as the fundamental pulse, in such a way that the null crossings of the Sinc are aligned with the centers of a subsequent pulses (for zero inter-symbol inteference while getting the frequency limiting abilities of the Sinc pulse). The longer you can make the Sinc pulse in duration, the tighter the bandwidth as in the extreme of an infinitely long Sinc in time would result in a brick-wall spectrum in frequency.  

This is demonstrated clearly in this graphic below, for a muli-level PAM waveform (Or what it actually is, is the real part of a 16-QAM waveform). Regardless the fundamental pulse shape for the blue line is a rectangular NRZ pulse in time, and the blue spectrum shown is what I was explaining above for the case or random non-repeating data. 

The red line is the "Raised-Cosine" pulse shape which is a Sinc pulse that has an additional taper given by a "raised cosine" (see additional graphic on that). But notably see how significantly more constrained the resulting red spectrum becomes and hence the pulse-shaped waveform is more spectrally efficient. We go through the extra effort to shape the pulse in order to conserve spectrum.