I finally received my iPhone4 today and sure enough, my Griffin PowerJolt Plus car adapter wouldn't work with the Apple Bumper installed. It just wasn't getting the required penetration with the added thickness of the Bumper. I found that if I applied pressure to the connector it would charge but as soon as I relaxed my hand it would break the connection. So I knew it was close. 
Since the iPhone end of the power cord is nice hard plastic, I got out my Dremel Tool and with a tiny grinding wheel I removed about 1/32 of plastic from the face of the connector body where it comes in contact with the phone. It now fits like a charm and makes a solid connection.
Since the iPhone end of the power cord is nice hard plastic, I got out my Dremel Tool and with a tiny grinding wheel I removed about 1/32 of plastic from the face of the connector body where it comes in contact with the phone. It now fits like a charm and makes a solid connection.