
I feel like the "can't buy 0" rider on Old Bridge is really only there to justify the card costing $1. It will almost never come up when trying to buy any other card, and just because you can't stack copies of a card doesn't mean it's balanced. Candlestick Maker and Ducat are both comparable to this (being non-terminal cards that give +1 Buy), and they both cost $2. Herbalist is also similar, and it doesn't even replace the action. I think you're undervaluing the bridge effect.
I also don't get the flavor. "Old Bridge" conjures to mind a rickety bridge that can't take too much weight, yet this card says that it can't take too little wight?
I think that the simple "+1 Action +1 Buy, cards cost $1 less this turn" card would be a balanced card for $4 that is comparable to Bridge: initially the +$1 of Bridge is stronger than the +1 Action, but it is significantly easier to build a megaturn when you don't need so many villages (or you can use the villages to support e.g. smithy variants). Also note that, similarly to Bridge Troll, there would be lots of stuff bought for $0 in the last few important turns, because Coppers are usually trashed and getting a Silver / Gold is almost always weaker than yet another copy of "+1 Action +1 Buy -1 cost". Personally I would dislike this card, because it is too centralizing: the optimal strategy is to trash quickly, get as many copies of it as you can, and then empty three piles. (Other cost reducers are more complex: with Highway, you need to get Buys/gains, with Bridge, Inventor and Bridge Troll you need to get villages.)
I added the "can't buy 0" condition to rule out decks that use this card as the only payload and make pileouts a bit more interesting (taking the last Estate may be difficult...). And once this condition is present, the cost of $1 ensures that it is easy to get the first Old Bridge, but it is difficult to buy up many copies of it quickly (unless there is another strong source of +Buy) – which mirrors the fact that the first copy of this is relatively weak, but many copies are very strong together.
These mean that Old Bridge differs from the existing cost reducers in the following areas: (1) it does not help gaining more copies of itself (2) it needs more $ production than other cost reducers and (3) it is less effective for pileouts (you cannot buy up the Estates or last few copies of cheap action cards).
I completely agree that the name "Old Bridge" is unfortunate – it fits the low cost, but does not fit the "cannot gain cheap card" effect. Does anyone have a better idea?