What BullGuard version are you using ?
What I will ask you to do, is to increase the Servers Timeout from Outlook Here is what you need to do:
1. Go to Tools -> Select "Accounts...".
2. In the new window, select Mail tab and then choose your account.
3. Click on Properties from the right-side of the panel and select Advanced tab.
4. In the Server Timeouts section, move the cursor to the maximum of 5 minutesm, then try again to send emails and let me know whether the situation improves.
Also, The issue may occur due to the fact that your emails are checked through both Real-time file monitoring and Incoming and Outgoing email monitoring. In order to fix this problem, please do the following:
1. Open BullGuard.
2. Go to Antivirus section > Protection tab.
3. Uncheck the Incoming and Outgoing email monitoring options, in the right side of the window.
Waiting for your feedback...