Asteroid Spaceship

Wouldn't we need permission from the asteroidians?

Your idea is not unique. It has been imagined in science fiction, and at least 20 years ago.

The problem isn't the technology, its funding it and applying it.
We monitor a TINY % of local space in search for potential earth-killers and even the largest are hard to detect and keep tabs on.
Most are virtually undetectable, due to their composition. Rogues get slammed out of the belt all the time and they travel at massive velocities, the likelyhood of salvation is slim (very slim).
Apothis passes within 30k miles from us in 2026 and will return in 2029, only when it first passes will we learn if it'll hit us on its return, but it is unlikely joe public will be informed if such is the case.

Ps Dates may be out a bit. I lost interest a while back.