Is there any code to link the Ubuntu One logo from my blog so that I can access it from there whenever I want and also to promote Ubuntu One?
The image on the bottom-right of the UbuntuOne site can maybe serve you as a logo. And putting that in-between link tags making the logo point to UbuntuOne can maybe serve your purpose. That way, if you are logged into UbuntuOne, your dashboard will directly open up giving access to your files. If not, then, will take you to the UbuntuOne homepage
Something like this:
Not sure if it's a copyright violation of some sort, so please do confirm that there is no violation of any sort before you put this into action. This answer is just to prove you can do it.