How long would it take for a transaction with 0 fees to be confirmed six times?
Dont worry about that. If you check blockchain.info at your transaction you will see it has medium-priority, which is the reason why it was send without transaction fees:

https://en.bitcoin.it/wiki/Transaction_fees

I normaly send transactions without fees, it can take some time. For me it was no longer than 6-12 hour until it got included into a block. If it got inlcuded (1 confirmation) it will get confirmed again every block. So after it was included in the chain you only need to wait 60 minutes for you 6 confirmations.

If your transactions need to be send quickly you should add some optional fees on them, which can be set in the options of bitcoin-qt (if that is your wallet).