Does the bonus show up anywhere after you build the ship, so you can look at a ships stats and know if it has the bonus?
I haven't seen the applied bonus mentioned anywhere on the Ship Details screen. I mean there is no "+??% Starship bonus" notation in ship information. You will find that on the Planet Details screen, though.
The only way to know if a ship has the bonus is to compare the stats to a similar ship that was built on another planet. It'll be noticible in the Attack. Like one of my dreadnoughts (upgraded from a Lucky Ranger) had 330 Attack, but a similar model dreadnought that was built on the planet I had the starship bonus had a 425 Attack.