It's called LAG.
How can a 1 minute game last for 3 minutes???

I doubt it. It sounds correct to me. You have one minute on your clock and your opponent has one minute on their clock which accounts for two minutes. You say you started at 3:43 but I'll suggest that it might have been something like 3:43:15 which would finish the game at 3:45:15 which is pretty close to 3:46.
You see the difficulty here? We're talking about such small spans of time that you'd really need to be keeping track of time by the second in order to either convince yourself that you made a mistake or convince yourself that it's a time bug. Without doing that, you can't really know.

Guys, it's just lag. You may notice sometimes when you're playing that it takes a moment for your opponent's clock to start after you've moved?

how do you know it is not 1 sec from 3:44 when it started, one sec into 3:46 when it ended?
That's the reason I mentioned that I saw the time properly.

you moved, how much did it take your opponent to respond?
more than 20 secs lag on a bullet game is very bad.
I have no idea how long he took to respond, but it was a 51-move game. Here's the link: http://www.chess.com/livechess/game.html?id=326545540
Yeah, 20 sec is too much.

How long did you and your opponent take to make your first moves? I don't think they count as part of the 2 minutes.

That's a good point, Eris. Clocks don't start ticking until the first moves have been made. The white move needs to be made within 10s otherwise the server considers the game abandoned but I'm not sure how much 'free time' is available for black's response.

How long did you and your opponent take to make your first moves? I don't think they count as part of the 2 minutes.
Yes, I forgot that but I presume it was around 5 seconds. He didn't take too long for me to say "Oh well, why do you accept it when you're not gonna play?"
I responded instantly.
I recently played a 1|0 Bullet game (less than five minutes back) and just simply glanced on the time on my laptop. It said 3:43 PM (and I know it just went to 3:43, not that I saw it on the 59th second). I sent out a seek, it got accepted within less than 7 seconds and we started. At the end, I won on time and I had about 5 seconds left on the clock. But when I instantly looked back at my laptop time, it said 3:46 PM.
So how is this possible? Is this some kind of bug? A time-delay bug?