When bombs are in play, if the movement template does not touch the bomb and the final position of the ship does not overlap, does the bomb still trigger if the base flies over it during movement?

No. There is no such condition within the game as "the base flying over". You pick your ship up from one end of the template and place it at the other end of the template. There is no base overlap happening in between those two steps.

From the FAQ:

Quote

Q: When a ship executes a maneuver, is the entire width of the ship considered to be moving along the maneuver template and possibly hitting obstacles?
A: No. Only the maneuver template itself and the final position of the ship are considered when determining if a ship hit an obstacle.

The same would apply to bombs.

Ty. I couldn't seem to find it in the FAQ.

8 hours ago, iamzoner said:

Ty. I couldn't seem to find it in the FAQ.

Buried near the end.