Simple Solution of Complex Problem
Here is that complex looking problem!
Everything built, written or designed in the given problem is to distract you from basic physics formula.
Speed = Distance / Time
Hence,
Distance = Speed x Time
All the details given except speed of bug & time for which it traveled are there to confuse you. Speed of bug is 1 m/s & it traveled for 1 hour = 3600 seconds.
Distance = 1 x 3600 = 3600 m
So the total distance traveled by the bug is 3600 m.