When to give a 2 week notice

Trying to leave my current crappy job...long story BUT

Im currently interviewing. Finished 1 interview, it went great. They did my background check last week and called my references. During the interview, they told me it was a week long process and asked if i put my 2 weeks notice in yet...i have not since i wasnt "hired" yet plus I have another interview at a different job this Thurs.

Im just conflicted on when to put in my notice. Im waiting to see the benefits and pay at this other place. It appears I got the 1st job in the bag...

The issue:

My boss is literally never around, always vacationing. He has been gone for over a month now.

I like to be polite and give a 2 weeks notice but I dont have a manager at my job either. I figured I would just leave a printed notice for when my boss' assistant comes in to do pay roll. By the time they would get my notice, a week would have gone by anyway lol

I dont feel bad, I just dont want to burn bridges :/