How long does it take for a ripple bridge transaction to clear?
Bitstamp BTC on ripple -> bitcoin address
Currently, the only functional bitcoin bridge the client directly uses is operated by Bitstamp. The time until they issue a matching bitcoin transaction is completely dependant on how well Bitstamp's automation and bitcoin transaction batching is working.
The Ripple side of the transaction completes within seconds. When Bitstamp is operating "correctly" the bitcoin transaction is initiated within seconds or a couple of minutes. Then of course you'll need to wait for however many bitcoin confirmations the receiver requires.
Once the Ripple side of the transaction completes, if there are any further unexpected delays or problems the sender will need to enter a support ticket with the brigde operator (Bitstamp for now) to have someone there look into the issue/problem. For example, a week or so ago, their automation stopped processing most Ripple transactions and it took quite a long time for their support to straighten everything out.
I tried it... ~ 2 hours before the bitcoin transaction is published.