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The answer is that from the perspective of the bowl, the photon would be massively blue shifted as it came towards the bowl, and then red shifted as is goes away.
Essentially, if you race towards a photon it gets more blue, and if the photon races away from you it gets more red.
Mentally, it feels as if the photon OUGHT to be moving in the same direction as the bowl, at the same speed, and that therefore it ought to "pool" in the bowl.
In truth, because all photons look like they're moving at c regardless of the observer, the difference is expressed in terms of a change of wavelength (i.e. Doppler shifted). The bowl will never quite catch the photons, and taken over an huge timescale, the photons will be almost infinately shifted to the end of the spectrum - becoming gamma radiation.
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Overhead, the Albatross hangs motionless upon the air,
And deep beneath the rolling waves,
In labyrinths of Coral Caves,
The Echo of a distant time
Comes willowing across the sand;
And everthing is Green and Submarine
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