That's the new way your document size is handled - works in some instances, pain in the ass in others.
This is the other.
To export object only, select the object, then go to:
Object > Slice > Create from Selection
Then when you export, just select the slice with your object.
Or, copy your object, switch to Photoshop, New Document (the size will match the clipboard), paste. Save for Web.
Hope that's what you were looking for.