According to the designer of Dominion, Donald X. Vaccarino:
Bridge makes all cards cheaper, not just ones in the supply. This was to prevent problems in weird situations. I am not sure the kind of thing you'd need to get those problems will ever happen, but I knew that this way of doing it meant I was safe. This also allows some unusual combos to work.
Which non-supply cards does he refer to? The only example I can think of is the Black Market.