I am bringing my fiancé home from Eastern Europe under a fiancé visa. I am wondering first: how to bring her money over, her bank charges a .3% on anything over 5000 euros, and 15 euros under 5000. It seems cheaper to send in increments of 5000 at a time, but will this make the government suspicious of us? Second: she is not a US citizen and won't get that or her tax id number for a while. Will she have to pay taxes on her money that she brings over? It wouldn't seem fair to tax all of it since she didn't earn it in America and had no affiliation. Any help anyone can provide would be much appreciated.

I don't see how it's cheaper to transfer the money in increments of 5000. 0.3% of 5000 is 15.
You also need to consider that the US bank also charges a fee.
There is no tax on the money transfer itself.