Yes, bug is a Scrabble word!
...and is worth 6 points in Scrabble, and 9 points in Words with Friends
bug
Verb
1. Annoy persistently
2. Tap a telephone or telegraph wire to get information
Noun
1. General term for any insect or similar creeping or crawling invertebrate
2. A fault or defect in a computer program, system, or machine
3. A small hidden microphone; for listening secretly
4. Insects with sucking mouthparts and forewings thickened and leathery at the base; usually show incomplete metamorphosis
5. A minute life form (especially a disease-causing bacterium); the term is not in technical use