I have just sent a bulk e-mail to my members and I discovered afterwards, that it was sent twice to each member. I am trying to find out what could have possibly caused this. I am sure I did not press "resend" . It's the second time this happens. It did happen when sending the very first bulk mail as well.

I used the standard setting = all members get an e-mail regardless of their number of posts etc...
I also run a staging environment on a subdomain based on a separate database. But I cannot imagine, the system would use this installation for sending mails as it is a totally separate instance of IPB. 
Any idea why mails are sent twice?

Thanks!

Check your System Logs to see if anything was logged. Also, you can disable all third party applications and plugins and try again to see if it happens without any customizations installed.

Thanks for this tip! I haven't found any errors in the system log related to the bulk mailing system. I will try it next time, by disabling third party applications.