I think both you and your opponent got way distracted with the available actions on this board.
- The most important action is Bridge, but you also have to get that draw up, and you usually want to do that first.
- All actions you really ever want cost 4$ or less here, so Ironworks is a worthwhile opening. Maybe you could skip it, because you can have extra gains from Bridges, but Ironworks is pretty good because it's non-terminal if you take actions, and you want to take actions until the very end (and then you probably have plenty of actions and plenty of Bridges and can Ironworks for Colonies!). So I guess you want at least 1 Ironworks, maybe more, but then the other cards (Smithy/Bridges) are probably more important
- You should never take a Vanilla Village here unless Fishing Villages are out. Although FV doesn't draw it is far superior and especially in an untrimmed deck it helps a lot to have that +Actions available if you have only terminals in your next turn's hand.
- Trashing is really lacking, but as said FV helps somewhat, and there's also Cellar which is nice, although I don't think you need that many.
- Mine is generally better in a Colony game, but you overvalued it a lot. I think you should skip it completely here, the other components are too important.
- Always remember, that you don't have to take a 5$ on a 5/2. Like here, opening Mine seems pretty bad. Maybe opening Festival could be okay, but I guess I'd cry into my pillow opening Ironworks anyways.
How I'd play this, probably still far away from perfection, though (It's pretty hard to give complete instructions and a lot depends on how the game is going):
Open Ironworks/FV on 4/3, Ironworks/Cellar on a 5/2. If you didn't open FV, get a FV asap. Get a Smithy and a single Bridge. Don't buy Silver, rather get more FVs. Don't buy Gold. Get more FV and Smithies. If your opponent doesn't seem to follow on Bridges like yours did, get another Ironworks. Get a few Cellars. As soon as you can get through your deck well, get a bunch of Bridges and sufficient Villages to play them. Maybe you have to fight them a bit earlier to not lose the Bridge split too heavily. Maybe a late Platinum can help if you split Bridges and neither can get through their decks well enough or if you have to buy Colonies, but this should be your last resort. Maybe you can't wait to pile out Provinces because 3-piling is imminent with lots of +Buys and Ironworks gains around, but you should delay going for green as long as you can.
/E: Seems like eliegel disagrees with my approach due to the lack of trashing. I guess I'd try it this way anyways. Maybe you can't get that mega big turn but I feel like you could do better than two Bridges.