How to find out why it takes so long for the sign in form to appear after opening the lid on my Macbook Air
The MBA goes into hibernate mode after several hours of being asleep. Also, if you close it and then open it again rapid the computer will be mid-cycle in going to sleep and will want to finished that before attempting to wake up (which can take some time also). In general Macs today take longer to boot up than they did, but they sip much less power when not being used. 

A similar post is here:

MacBook Air takes an eternity to come out of sleep

And some solutions are posted