For the most part, when you start a bittorrent client, bootstrap off of:
- nodes from your last session, that were saved to disk
- other peers that you have on any of the swarms you're on
There are a few well-known bootstrap nodes which clients can use if they have no other means of finding any. Essentially the only case this happens is when you install a client for the first time, and the first torrent you download is a magnet link without a tracker.
You can then hit router.utorrent.com:6881. I believe transmission, azureus and bitcomet run similar routers, and possibly other clients as well.
By "router", I mean a node that appear to behave like any other node in the DHT, but probably has a different mechanism for determining which nodes to hand out, and probably is optimized specifically for the use case of just introducing dht nodes to each other.
UPDATE: you can run your own DHT bootstrap machine, here's the source code.