pester vs bug

pester is not a noun while bug is a noun.

Word	Noun	Adjective	Verb	Adverb
pester	No	No	Yes	No
bug	Yes	No	Yes	No

As verbs, pester and bug are synonyms defined as:

Other synonyms of pester include badger, beleaguer, tease.

pester (noun)	bug (noun)
	insects with sucking mouthparts and forewings thickened and leathery at the base; usually show incomplete metamorphosis
	general term for any insect or similar creeping or crawling invertebrate
	a minute life form (especially a disease-causing bacterium); the term is not in technical use
	a small hidden microphone; for listening secretly
	a fault or defect in a computer program, system, or machine

pester (verb)	bug (verb)
annoy persistently	annoy persistently
	tap a telephone or telegraph wire to get information