The "bureaucrats in Brussels" are nominated by EU Parliament members, who in turn are elected every five years directly by citizens in European elections. They are there not because the EU is anti-democratic, but because you cannot realistically expect elected representatives to deal with every single detail. Otherwise, you would be in a direct democracy.

Doesn't the same thing happen in the US? Federal and state agencies are full of non-elected employees that take impactful decisions on a daily basis, but I don't see many Americans complaining about a lack of democracy in the USA because of this.