‘You only use 10% of your brain’ is only referring to the physical areas of your brain. Which is not true, because we have scans that can show that we use all areas of the brain.
I always thought that saying was referring to how we only use 10% of our brains potential.
There is too many different versions of starship troopers to have a meaningful conversation about the logistics of how they travel. But there are transport bugs capable of interstellar travel. The first one was located on Pluto, so they were already in our system. Depending on which version of Starship Troopers you bring up Buenos Aires was either attacked directly by the bugs or had a meteor destroy it.
And the bugs have to have some sort of FTL travel since the humans followed the first transport bug back to the Arachnid homeworld. If that would take billions of years then the humans wouldn’t have been able to follow them back after they left Sol.
Starship Troopers is full of plot holes and inconsistencies that would, again, likely prevent us from having a meaningful conversation about the logistics of the Arachnids.