We all know that KC-KC-Bridge-Bridge-Bridge is a killer, killer combo. But it's so hard to pull off. There is, however, another extremely reliable way to get many Bridges played in the same turn, and that is through the use of Native Village.
This is more of a total-game-strategy rather than just a little combo. You want to start NV-Bridge (you can do this on either 5/2 or 4/3, which is nice), and then simply keep buying those cards, and more or less only those cards, for the rest of the game.
Every time you play Native Village, always choose to set aside the card. What you're going for eventually is to pick up a massive native village mat, play a ton of bridges (fueled by the actions from NV itself), and win.
There are a few ways you can look to win, and you really need to watch your opponent for that. If they're going for a rather conventional strategy, like big money, you want to hold off on "going off" for quite a long time, so that you can get like 6 bridges (or maybe even more) in one turn and just scream through the provinces and win.
In the mirror matchup, you have to be VERY careful about the game ending on piles and/or be ready to set the combo off what seems like prematurely in order to three-pile and win. In general, three piles are something you always have to watch out for, as the native villages and bridges themselves are going to go pretty quickly, and with so many extra buys, you can easily run out even a fairly full pile pretty quickly.
This combo is very powerful and pretty fast, but it has some limitations. First of all, it's somewhat vulnerable to curse-givers and other deck-bloaters (see ambassador). On the other hand, if you adjust by increasing your NV ratio a little, you can actually trim this a little - not that I'd suggest it against a good curse-giver, but you could probably hold against a weaker one, like Young Witch (needless to say, if NV is the bane, this is a no-brainer).
As for speed, it's pretty fast, but maybe not chapel fast. In fact, I don't know all the baselines for chapel OR for this combo, but I'm guessing this actually beats a standard chapel/big money setup, but you may need to do this with a little guile. For instance (and this is not uncommon with this combo), your chapelling opponent has 5 provinces, a chapel, and money, and you pull the trigger on your combo. If you can get 6 bridges played in a turn, that's enough, even without any money, to buy 3 provinces and 4 duchies, which is as much VP as the 5 provinces, and your 3 estates will win it for you.
Other cards to add to this combo: Well, generally you want to get the native villages and bridges first. Of course, an early Lab or two or three is going to help, but in the most common scenario for this, c+c+c+bridge, it may well be better to grab a bridge and a native village than the lab plus nothing. Of course, any other type of village is going to help, especially in the mirror, but again, you need to prioritize the main combo elements. Cities throw a monkey wrench.