Actually, Nokia has a free software for synching (and other functions). Used to be called Nokia PC Suite when I used it; it's morphed into Nokia ovi suite. I can't find the 3110 (is it a US model or other country?) but 3100 and 3120 both listed. Nokia USA - Nokia Ovi Suite
I used Nokia PC Suite with my Nokias to synch between the phone and Outlook long before I ever even thought about getting a Blackberry. Once you get the info synched with Outlook, using BB Desktop Manager to sync with the BB will be a piece of cake.
If you have specific questions about the Nokia or using Ovi Suite, you may want to ask on the Nokia forum on Howard Forums. http://www.howardforums.com/forumdisplay.php/39-Nokia
BTW -- just re-read your post. Not sure you can do this with Bluetooth but may need a cable for the 3110 to the PC.
Edit: Read OP post AGAIN and realize OP is in UK so correct link is http://www.nokia.co.uk/support/downl...ware/ovi-suite
. And 3110 is listed.