Hello there. This isn't actually directly answering your question. I had a recommendation actually semi-related to your question. The efficiency and control issues related to ion engines powered by nuclear power give it substantial advantages relative to direct thermal nuclear propulsion, particularly in the heat regulation issues. I bring this up because ion engines have nearly already had there research completed, nuclear reactors have nearly had there research completed in some forms and had it completed in alternative forms, and it would be a much cheaper alternative propulsion system while being just as useful for today's and the next hundred years requirements in space travel. This combination, ion engines powered by nuclear reactors, would likely give us complete access to everywhere in the Solar system in convenient time. It would also be worth stating that if you were thinking of travelling beyond the Solar system, using Solar Sails with reflectors nearby the Sun would get you just as far for mush cheaper making the deceleration the limiting factor upon arrival with regards to your ability to travel between star systems, and this could be equally as well addressed with the nuclear powered ion engines. Shipping the reactor parts into space, constructing it in space, then using it to power ion engines to travel would be a great way to ship freight to or from Mars for instance. If you happen to be Elon or Jeff, I would recommend this. Building a reactor in orbit piece by piece, then using it to power the ion engine equivalent of a space train to ship your freight back and forth to mars might be a major cost saver. This way BFR or New Glenn only have to get to orbit, then land again, then delivery the next shipment to orbit rather than having to travel all the way to Mars and back. The "space train" would ship all the supplies and people to Mars and back, with only a few rockets being required on the Martian end just to bring the people that wanted to return back to the ion engine "space train system" which would be travelling back and forth between Martian and Earth orbits while never actually entering into the atmosphere themselves.
If you are neither of them, keep in mind you could do the same thing, but working with what they already started. This is to say, hire one or the other to ship the parts up one at a time, or maybe even design and develop them for you. You could own the "space train system" that they use for freight while they own the rockets and various assorted tech.
This being said, nuclear propulsion has already been researched to some extent, but has some serious limiting factors in many of it's forms. The biggest being cooling and control issues. There would still be extensive expenses required for many of the thermal nuclear propulsion systems, but some have actually been completed. If you were utilizing it in atmosphere, it would be very different than if you were using it in deep space. There are no regulations on or in deep space travel nuclear reactors at this time. In atmosphere propulsion is a different story and has nuclear governing bodies depending upon the nation you are in as well as it's respective international treaties. The US has banned it. You could probably get a nuclear agency to approve it in combination with NASA, which would then recommend Congress accepts it.