I can't find my audio book I downloaded from iTunes Store on my ipad

It should have downloaded into the Music app (the iBooks app is for ibooks and epubs/PDFs) - when you have audiobooks on an iPad you will get an Audiobooks option under the More button at the bottom of the Music app.

Note that audiobooks are currently a one-time only download from the store (so they won't appear in the Purchased tab for re-downloading), so you may want to copy it to your computer's iTunes library via File > Devices > Transfer Purchases so that you can take a backup copy of it - it should copy over to the Books part of your iTunes library (or the Audiobooks if you are using a Mac with OS X Mavericks on it).

Does Audiobooks show across the bottom of the Music without going into the More button ? And if you try playing it via the spotlight search does that take you into the Music app ? You could also try closing the Music app via the iPad's multitasking bar and see if you get an Audiobooks option when you re-open the app.