I'm not up on whether it's a good idea or not, but normal banking international money transfers are completed using IBAN/BIC numbers which you can get from your bank, not your normal bank details.
If I remember right, there was a scam a while back that related to some forms of transfers taking a while to complete. Money would appear in the account but not have cleared, giving a window to cancel the transaction and reverse the process. Make sure that the money is cleared funds genuinely transferred.
There's a lot online about money transfer fraud if you google it, and I think certain methods are more prone than others.