We need acceleration to about 300-500 m/s relative to an NEO asteroid - to get to an LEO.
What is needed is the lightest package possible, that includes engine, fuel tanks, control module and thrusters for maneuvering.
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With 2020 era tech 'most fuel efficient' with a nuclear reactor available is probably some form of ion engine.
Taking the X3 engine and most generous numbers from here we get a thrust of 5.4 Newtons and a fuel consumption of .2 grams a second. 5.4 newtons on 100 tonnes gets a per second acceleration of 0.054 mm/s, so our 300ms burn is 5.5 million seconds or 64 days and around a tonne of Xenon, so we do not need to venture deep into the rocket equation.
Note that is several million dollars in Xenon for 100 tonnes of payload, so less efficient gases may be better if this is intended to be sensible cost wise.
The X3 needs 100 kw of power, so using 10 of these masses 15 tonnes so the amount of Xenon needed to do a minimum escape burn from earth (3200ms) for our 20 tonne (15 for engines, 1.1 for fuel coming back, 4 tonnes structure) of craft involves several months of departure burn and several more tonnes of xenon, realistic intercept and capture probably involves another month of burn and tonne or so of Xenon.
The 2040 most fuel efficient solution probably involves harvesting mass from the asteroid to power the flight home, but in 2022 there are a lot of unknowns in how to process a rubble pile into usable fuel (and ideally structure, power plant and engines).