I have been searching and playing with my site for while, but I cannot work out how to allow a registered member to edit their own profile on our J!/CB/K2 site?

When I link to the user page, it goes to CB, so I cannot edit it there.

Any suggestions?

Have you tried the K2 user module?

Doh!

I have been focussed on a menu option solution, as I wanted to create a contributor menu with some additional options, such as blogging guides. I see this can be added to the module, though

Anyway, I have added the module to user pages and have got 4 options/bullets, with only 2 populated!

It is also saying that I have ) contributions.

See the screenshot

www.yourbusinesscommunity.co.uk/images/k2.png

This is a template issue (check the hovering block).
The template you are using is creating a conflict with Joomla!'s default modal. This is something that should be addressed by the template's developer.