Yes, especially the Golden beetle and Hercules Beetles are usually the best bugs to turn in.
But be careful, they appear in the evening, and the Bug Off ends at 6.
BUT there's also a chance neighbors can beat those with good bugs. (for me I almost lost to Stinky's Oak Silk Moth which had 5 more points than my Golden Beetle because he got extra points for each criteria)
Palutena: "I really can't imagine you being in a "melee". Pit: "That's because I wasn't -_-" 3DS Friend Code: 0430-9368-3384
is there any point doing the bug off again if you already have the gold trophy?
or are you just trying to get a personal best?
Every time you give Nat a bug worth 80+ points that also beats the 1st place score, he gives you a piece of the bug set. IIRC you can get up to 6 pieces of the set during each Bug Off. So, if you give him increasingly more valuable bugs while also beating your 1st place score each time, then you can keep getting the items.