Not only is there bonus experience, Squirt, the infamous trainer, visits on November 15th (US) and November 16th (EU).
Why is this significant? Squirt is the only garrison trainer that awards Cataclysm/WotLK trainer amount of pet experience. You can battle her repeatedly within the comfort of your own garrison. Need to heal up? The Menagerie NPC located right next to the battle has you covered. Squirt's visit during the Bonus Event is just a very efficient and convenient way to level a massive number of pets!
For mathy stuff on the experience gain from the Squirt battle per pet level, see this post on WarcraftPets. Also in that thread, a quick and easy carry pet strategy for that particular battle.
In addition to Squirt's visit to the garrison during the event, the Hallow's End Creepy Crawlers decorations are still active. This means there are plenty of wild battles just waiting inside your garrison (or someone else's!) just waiting to award a decent chunk of pet experience. They respawn instantly, so it's super convenient. These battles also reward progress towards Draenor Pet Brawler (monument achievement).
This month's Pet Battle Bonus Event in a nutshell: Level lots of pets conveniently, make progress on the monument achievement, and you can even use the wild battles to level your toons! So effective, so much efficiency...it almost brings a tear to my eye. :')
Which Pets to Level?
So which pets should you level during this awesome week/weekend? Well, it all depends on what your goal is. Just getting started? PVP? PVE? Both?
For PVP, you'll need to check up on the current meta, that is, which pets are currently the most used and/or effective in pet PVP. The meta can change over time as new pets are released. Discodoggy's website is great for potential teams; he puts a lot of work into creating and testing a wide range of different team compositions.
PVE, WarcraftPets has a list of top 20 pets for battling (as rated by our users). This list is a good starting place for both beginners and those heading into later and tougher pet battle challenges.
Lio's top 10 wild pets is a solid list of pets that will come in handy in different situations. If you haven't taken a look at these pets and/or leveled them up, perhaps you should and what better time than during the bonus event.
Looking to complete all of the trainer battles (up until WoD and excluding those in the Celestial Tournament)? Check out WarcraftPets' community guide to all of the Grand Master trainers and how to defeat them using a carry pet. It may give you an idea of which pets you need to make a priority in your leveling adventures.
For the Celestial Tournament, I suggest heading over to Wowhead and reading some of their user-written guides on how to defeat the rotating trainers. Much like the Grand Master carry pet guide above, these guides should give you an idea of which pets to prioritize leveling.
If you want to level pets, any pets, then do it! Don't let these recommendations hold you back. Level and use whichever pet brings you the most happiness. :)