Sending a product on the Apple Store as a gift to a friend? I want to make a purchase from the Apple Store as a gift to my friend. The purchase is a physical item (e.g., iPhone), rather than an app to download.

Because I live far away from her, I want to use my Visa credit card and send it directly to her address with the option of "Gift" selected. Would that be possible? I will be using her address instead of mine. So, what would the transaction look like when I check my Visa transactions at my bank? Would her name appear on the transaction? Would I still be able to send it to her directly with her information, or do I have to send the package to myself, and send it to her after that?
You have multiple questions here.

First see Apples instructions here http://store.apple.com/us/help/gifting

Will your Bank show and what, you can answer that based on prior experience. My Visa shows the Store name and the amount, not to whom is it shipped or what it was.

In your case better option might be a Gift Card, that you can mail your self, thus no trace.