It's my understanding that there were in fact iron objects being made during the bronze age, but I don't know much else about bronze age iron-working. What types of objects would have been typically made with iron at that time? Are there certain types of objects that would be made in iron but not bronze, or vice-versa? Who was likely to own objects made of iron, versus objects made of bronze? Was one more affordable than the other?
Early iron wasn't particularly better than bronze. In fact, crude iron is often softer than bronze. As both copper and tin melt at low temperature, bronze is easy to work with. It's also easy to mass-produce objects in bronze, where early steel was close to alchemy and requires very skilled smiths to work it properly. Furthermore, bronze doesn't rust. There are 3,000 year old bronze swords that are still usable. The earliest iron swords are mostly dust.
So far I'm answering a question that you didn't ask, but but it's important to establish that there wasn't a huge technical pressure to switch from bronze to iron. The bronze age actually came to an end due to more a more mundane force: availability.
Tin is pretty rare and unevenly distributed. Europe in particular is tin-poor. For the Romans, this wasn't a problem, as they could import whatever from wherever, but as the Empire broke down, so did trade routes and people had to make do with what they had at hand, which in this case was iron.
So the real answer is this: if you lived near both tin and copper, the bronze age was slow coming to an end. If you didn't live near tin* and copper, then you couldn't make bronze and therefore most (or all) of your metal implements were made of iron.
*: Not entirely true. You can also make bronze with copper and arsenic (cleverly called arsenical bronze) but the arsenic compounds necessary were just as difficult to come by as tin, so the same rules apply. Also, arsenic is poisonous and tended to kill the smiths working with it.