"Your giant bb-gun would require a motor to cock the thing. And it would have a lot of moving parts. I think a mass driver would be less complicated and less likely to break down."

And the motor would need some source of power- such as electrical [get energy from the sun] or chemical [you could bring it there to be used or mine it there- you also bring a nuclear reactor as source of electrical power or use the steam power directly as mechanical energy].

Chemical energy is simply a way to store energy- as is a spring, a flywheel or battery.

You could say that chemical energy is very popular on earth because O2 in our atmosphere provides most of the energy- with a rocket or an internal combustion engine one is getting more than half of the energy from O2.

To move a space rock one should look for ways of obtaining energy which are available in space.
A primary source of energy in our solar system is the Sun.
All the energy we use is from the Sun or result of stellar "evolutions" of other stars [namely, nuclear energy].

[[ Though using tidal energy could be said to be using orbital energy [of the Moon] which is not as directly relatable to the fusioning process of stars.
Though one could argue that much of what allows one to have orbital energy is due to supernovas ejecting matter into the galactic environment
[in addition other star processes of emitting matter into galactic environment in which gas cloud condense into new stars and solar systems]. Though one could also say that without the force called gravity, one would not have the fusion reaction of stars, and therefore one could say that gravity is the sole source of all the energy we currently use on earth.]]

Anyways, on earth we mostly use solar energy which has been stored as fossil fuels and the O2 of our atmosphere- this energy has been stored for millions if not billions of years. Solar energy can also be captured in a more direct fashion with solar panels or solar furnaces, or solar energy can create wind or rain and this energy can captured by wind mills or hydro dams.
Another category of energy is nuclear energy.

And the final category of energy is geothermal or tidal energy sources which as related to the tidal action of the Moon orbit [and also the heat of the nuclear decay of the earth core].

In space we will use and have used what could be called orbital energy- and this is called using a gravity assist or gravity slingshots.

There is far more "orbital energy" in space of our solar system than all the O2 and fossil fuel energy ever generated on earth.
If we go into space we will without doubt use a lot of orbital energy.
So orbital energy in space will not be a bit player, as it is on earth with geothermal or tidal power plants.

So, an elementary or primitive way to use orbital energy to move a space rock is to hit the bigger rock with a smaller space rock. And there is no shortage of little space rocks- they monthly hit our planet.

So, instead of using springs to move some chunk of a space rock [the size of automobile or school bus] so it's moving at 50 to 100 m/s. One could hit the space rock with smallish rock the size of a school bus at somewhere around 1000 m/s or more. And thereby require less energy to get far more power to move the the space rock.