If you want the person to be banned from the channel, then speak to the channel operators. If you want to see the person banned from the network, then speak to the IRC operators of that network.
However, keep in mind that most people on IRC have dynamic ip addresses. Banning somebody permanently is not as easy as you might think if they want to evade.
Also, I would just recommend having your girlfriend putting the person on ignore. A lot of harassers get off by provoking a reaction out of their victim. They want attention. Don't give it to them and they will get bored and go off to do something else.
