The most common and most likely answer to this crossword clue is the 7 letter word BADGERS
I've seen this crossword clue in The Daily Telegraph
B
A
D
G
E
R
S
Buddy explains!
The straight part
We know that "Nocturnal omnivores that are black and white bugs" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case nocturnal omnivores that are black and white bugs = badgers.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does BADGERS mean?
BADGERS noun- Any mammal of three subfamilies, which belong to the family Mustelidae: Melinae (Eurasian badgers), Mellivorinae (ratel or honey badger), and Taxideinae (American badger).
- A native or resident of the American state, Wisconsin.
- A brush made of badger hair.
- (in the plural) A crew of desperate villains who robbed near rivers, into which they threw the bodies of those they murdered.
- To pester, to annoy persistently; press.
- To pass gas; to fart.
- An itinerant licensed dealer in commodities used for food; a hawker; a huckster; -- formerly applied especially to one who bought grain in one place and sold it in another.