Fun question!
With a hypothetically PERFECTLY reflective mirrored interior bulb surface and a PERFECT vacuum inside the bulb and a PERFECTLY indestructible filament,
I think everybody here concurs in these first few steps:
Electrons within the filament will continuously cycle from lower to higher to lower energy states as
the inflowing electricity continually pumps filament electrons to higher valences momentarily,
the electrons then collapse to lower valences and emit light as they hop down to a lower energy level,
that light will hit the reflective inner bulb wall,
and in direct response to the OP, QUOTE: In theory, wouldn't it 'fill up' and then eventually explode? END QUOTE, the answer is "no" because conservation of matter/energy would prevent any "mass" of emitted particles from exceeding that of the filament.
But then everybody does not concur on next events. My conjecture:
The photons will impart some of their energy to atoms in the reflective surface, pumping their electrons to higher valences.
Those electrons of atoms in the reflective surface will hold the added energy only momentarily, then collapse to lower valences, emitting the energy as perhaps heat and/or other radiations, to the entire apparatus, both filament and envelope. This will mostly be as heat.
The heat will diffuse throughout the bulb, but will tend to preferentially radiate outward away from the bulb toward the relatively cooler exterior atmosphere, seeking thermal isostasis, because the bulb's interior will be hotter, and will not absorb more heat.
Photons within the bulb, having given some of their energy to the reflector's atoms, will themselves step down in energy so as to no longer remain visible light, but something else in the EM spectrum of longer wavelength than visible light.
The whole thing could be useful to warm incubating chic eggs.