Photons as little bullets of light are not the most correct way to view light (though it is sometimes a very useful picture). A more complete way is to understand photons as the energy gaps between allowed energy levels in each plane wave that makes up the EM field. This isn't particularly easy. One thing I struggle with is how to handle the delay time of light between a distant source and a detector. Even classically this is nontrivial (at least to me). Pure plane waves exist in all space at all times. To get a localized wave packet requires the energy be spread over some band of wavelengths. How this happens in quantum theory of light is likely just the way it happens classically but I wouldn't mind a reference to walk me through it. In the end the quantum state of the field must encode/contain this time delay.
I think Mandel and Wolf's 'Optical Coherence and Quantum Optics' is a definitive source for the question being asked and, specifically, Chapters 10 and 11 on the quantized EM field. Other quantum optics textbooks are probably good sources too.
In a nutshell, your intuition is correct and a single photon nominally propagates like a classical EM field. I say nominally because the statistics describing the field, e.g., phase and energy, may have different interpretations than in classical field theory. And, like you say, pulsed photons can be described by a wavepacket of single photons spread over some bandwidth. The Fourier transform then gives the corresponding duration.
The delay itself traces back to properties of the medium, which can often be described by the susceptibility and the index of refraction.
Hope this helps.
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