Question
I have miniature red petunias in a 16 inch hanging basket.  They
have been doing quite well and still are.  I was just deadheading
them and noticed very very small white bugs on a section of them.  
I dead head them quite frequently, so I imagine they have just
arrived (the bugs).  I live in Southeastern Connecticut

Answer
Marcia,
If the bugs fly away, it's probably White Fly - if they're tiny and don't fly, it's probably aphids.  If it looks like cotton, it's either scale or mealy bug.  No matter which insect it is, the best thing to use is insecticidal soap or insecticidal soap that has neem in it.  Spray under and over leaves about every 10 days - keep fertilizing and deadheading and cut four or five stems in HALF every week.  This keeps plants full and bushy.  
I hope this helps,
C.L.