My personal "dream rocket" is to combine a dusty fission fragment rocket with the nuclear lightbulb concept. You have a subcritical fast dusty core which achieves criticality via a spallation neutron source rather than a moderator, using a compact linear accelerator powered by the reactor's fragment deceleration grids (no Carnot losses). The core radiates intensely in the mid-IR range. The core is suspended electrostatically in a fused silica chamber, which while it will steadily blacken in the visible from neutron radiation, is resistant to blackening in the infrared, and can tolerate quite high temperatures. Outside of the core are mirrored aluminum walls. The particles of nuclear fuel in the core being a fine dust, their ability to radiate quickly is extreme; if the process is designed suchly that they tend to radiate and absorb in different bands (a strong reverse greenhouse effect) then you can have ridiculous optical power output despite the radiative temperature only being in the infrared.
Such a craft could operate in several different modes.
1) Clean airbreathing: Air is shunted into the engine between the transparent chamber and the reflector. "Starter" microwave beams (powered by the deceleration grids) help ionize a thin sheath of air to plasma, making it more opaque to IR, allowing it to heat even more, generate even more plasma, absorb even more IR, and so forth. The superheated air exits out the rocket nozzle.
2) Rocket: Hydrogen or other fuel is shunted in instead of air; otherwise, the process is exactly the same. #1 and #2 can be hybridized, and also get a little more boost from any combustion that occurs in the process.
3) VASIMR-like: Only a low flow rate of fuel is injected. The low flow rate and high degree of ionization allow it to reach a much higher temperature and be directed out of a magnetic nozzle rather than being in contact with the physical nozzle.
4) Fission fragment rocket: The bottom of the core is opened up and fission fragments leave the rocket freely. This is of course dirty and low thrust, and would only be useful in space, but would yield absurdly high ISP while still achieving thrust levels comparable to today's ion engines.
5) Photonic rocket: If you want to go really extreme, you could simply just radiate the intense IR beam from your core running as hot as you can get it without melting the silica chamber or mirrored reflector. But I'm not sure if you'd actually get better performance, as you wouldn't be tossing your waste (thus lightening up the craft), and 3/4ths of the energy is already in the fission fragments. On the other hand, if you're willing to accept even less thrust, the simple decay of any short-lived isotopes inside the core will provide some thermal output even when your reactor is not engaged.
Another neat part of this is that being a fast reactor, it could breed its own fuel. So mined natural offworld uranium or thorium could be purified and milled into appropriate dust and then injected into the reactor; with time it'd breed into the fuel needed to power the craft. No need for offworld centrifuges or anything like that. Another capability would be to work around the anti-nuclear crowd on launches: if you face too much opposition you could launch your craft loaded non-fissile fuel, just natural uranium or thorium, and then mount it to a (very) large space-borne solar power source. You could then breed your fuel in space using the craft's linear accelerator. Of course, it'd be far better to just load it with fissile fuel on earth and then ascend in airbreathing mode.
A fission fragment reactor is expected to produce no waste when operating in fragment rocket mode excepting what fragments you decelerate for power generation. When operating as a closed system (with all fragments decelerated), the waste will still be low, as with any fast reactor, assuming that fragments are decelerated in an area well exposed to the core's neutron flux.
This is not the only "nuclear lightbulb" concept, but it avoids the problems with all of the others. It uses a practical, proven way to keep the fuel from contacting the "bulb" (electrostatically repelled dust) rather than a lot of hand-waving, and neutron blackening is not a problem due to the use of IR rather than visible or UV light. Dusty fission fragment reactors have been researched and simulated; however, that which was simulated was a slow reactor with a water moderator, not a fast subcritical reactor. So I can't say how well that aspect would play out. Also I've done no simulations on the rate of absorption of air or various fuels to absorb the IR on their way out of the rocket. I have little doubt that some configuration would work in that regard, but it's not something I've calculated out.