I don't have the experience to answer this (Political Scientist, not a Historian) but I think it would be helpful if you specified an actual date or concrete span of time.

The Aegean Bronze Age began around 3200 BC ("Ancient Greece". British Museum. Retrieved 2012-08-03), while the Bronze Age in the North Caucasus started in the 4th millenium BC (Philip L. Kohl. The making of bronze age Eurasia. Page 58) and the Unetice Culture in Central Europe was more like 1700 BC.

So, which of these periods are you interested in? Hopefully someone with more academic background can help out (and I hope I did this right and didn't break any rules. I love AH. Please love me back).

I'm not quite certain if you would consider them European, but the Egyptians have my vote.

During the Bronze Age, the power centers of "Europe" was focused in the Middle East. Think Mesopotamia or fertile crescent. It was also around this time, that the Egyptians constructed their Pyramids and Sphinx, some of the most recognizable and awe inspiring testaments to human ingenuity ever seen.

If you want to get technical however, and argue that Europe is restricted to modern day geographical definitions only, things get a little more tricky. As previously mentioned, the real powers of the European world were in the modern middle east, but a good case could be made for the Phonecians as well as they had settlements in many parts of modern Europe, albeit mediterranean parts but hey Europe is Europe. Why? The Phoecians had one of the earliest, most successful and most profitable trade systems ever developed. And their monopoly over Tyrian Purple, made from the secretions of sea snails gave them intense economic sway over the entirety of the mediterranean not really ever seen until the days of Carthage and Rome.

The only states worth that name in geographical Europe during the Bronze Age were Minoan Crete and Mycenae in continental Greece, which either conquered or vassalized Crete circa 1400 BC. So Mycenae.