For the strategy to work both [Crimson Spore] have to be level 25 and Rare quality.

[Crimson Spore] is one of the easiest battle pets to get. You can get one for each character in a treasure in Gorgrond (Draenor), by clicking on the [Strange Spore] object found at 57.1, 65.3. It can also be bought at the auction house and is usually quite cheap.

The first ability chosen for the first pet is [Creeping Fungus], although the alternative [Sting] also ends the fight in the same number of rounds. [Creeping Fungus] was chosen because in the case of a crit, one less DoT damage will be needed to kill the bear (although the number of total rounds is the same). The animation timing of the two attacks also seems very similar. There really doesn't seem to be a significant time difference between one option or the other.

The PetBattleLogKeeper addon has been used to calculate the combat time, both for [Creeping Fungus] and for the alternative [Sting], and for both cases the final time is practically the same, between 22s-23s, usually 23s. Here is a screenshot of various combat time tests. There are other alternative strategies on this page that also end in 3 rounds and use a similar double [Explode] strat, and most of these strats are probably just as fast as this one.

I put a more condensed functional version of the TD script below (the original is larger to cover the use of possible alternative pets in the future):
use(743)[round=1]
use(359)[round=1]
use(282)
change(next)
standby

Enjoy! (edited)