Let it dry! (I'm in norther Indiana, gardening zone 5) Hubby and Dad put up a nice new picket fence (cedar) 5 years ago and in my impatience for my white picket fence insisted we stain right away (against hubby's better judgement). Big mistake. Stain looked awful after second season, and recoating has become a problem. (After power washing and sanding, I was back out there the other day with furniture stripper. What a nightmare--gave up on that.) Our local paint store said just sand it better (going for orbital sander this time) and a new coat of stain should take alright (fingers crossed). This all could have been avoided had I been a little more patient and allowed wood to dry. Paint dealer reiterated what my husband said: best amount of time for wood to 'cure' is in summer heat- 3 months minimum is adequate, but preferably 6 months.
As far as bugs, not sure about that, but we had a bare cedar privacy fence here that was untreated for years by prior owner. No sign of insect damage. When we bought the place we power washed and stained it, looks great and still no sign of insect damage anywhere.