A hink pink is a word game where the answer is a pair of rhyming words that fit the given clue. In this case, a hink pink for a bashful insect would be "shy fly." "Shy" rhymes with "fly" and both words fit the clue of an insect that is bashful.
Shy guy
shy guy
Fly pie.
roach coach
fat gnat
What is hink pink of a rhyming pairs that stinging insect that doesn't cost money
"Snug bug" is a hink pink. A clue for that could be "comfy cicada" or "cozy aphid."
ant's pants
Evil weevil is a hink pink for wicked insect.
free bee
bug rug
free bee