Thermal Bridge Calculation question - if we only have one wall in a basement that is adjacent to the ground, how do you calculate the B' (Characteristic Dimension of Floor according to ISO 13370)? Do you still add up the perimeter of the entire basement, or do you only use the length of this particular exposed edge?

Just the length of the exposed edge.  13370 refers to P as the 'exposed perimeter'.  Note that according to ISO 10211, B' = 8m works for any floor where B' ≥ 8m, so in most cases like your example, you're ok to model 4m on the interior (1/2 B') and 20m on the exterior (2.5 B'). Hope this is what you're looking for (and it's not too late!).