Here are some of the ways you'll know if you play a bot.
They usually appear in patterns, so first you might see a standard deck (well known decklist / cards) with some odd ones in between.
This opponent might be really good or really bad depending on your ranking / winrate.
They will often play very fast and end their turns in almost an instant when they spend their mana. They even coin, do nothing from time to time.
They also use alot of the card backs released since Revendreth / March of the LK, and that includes the new Lich King ones (most popular for bots) as well as Hakkar and others, again depending on your rank / WR.
In about 3 weeks I think I've played against real people 10% of the time, the rest have been bots.
If you wanna test this I recommend you do it late at night. It's absolutely insane how we've gone from 6-7 min queues in Duels to now having an opponent almost instantly or within 30 sec.
Nobody is playing this game, and I suspect Blizzard have been doing Bots ever since it's inception. Inflates numbers, looks good for investors. Twitter did the same.
Please tell me you're joking.
"Sometimes they're good, sometimes they're bad, sometimes they play meta, sometimes off-meta, they use various cardbacks, they end their turns..."