I don't know how your relationship with her started, but I just want to throw this out there.
We live in a world where relationships can be had in many different ways. I'm probably the outsider on this one, but I don't consider a breakup over the internet to be that bad or cowardly. Here's how I see it. I absolutely sucked with walking up to girls and starting a conversation. That to me was just as hard and terrifying for me as breaking up with someone to their face is for others. I not only resorted to the internet, but to a fucking cellphone application in hopes that I could maybe strike up a conversation with a cool girl (paid off big time).
But my point is, it wasn't too long ago, maybe 5-7 years, when using the internet to find a partner was consider taboo, and in most cases it came with a negative stigma. I remember people (myself included) almost being ashamed to admit that I was using such services. People thought it was cowardly to have to look for females from behind screen. These days, it is the societal norm. Of my close group of 6 friends, 4 of us are in a long term relationship that started online. Looking at my girlfriend and I, although we have a house together, we still have 100+ text message conversations every day. So much of our relationship, literally since the beginning, has been made possible by our access to technology.
My girlfriend and I use technology as an aid to conflict resolution. Her and I are both very emotional people. The last thing either of us wants to do is hurt the other one, and that's very easy to do face to face. Especially if you struggle with thinking up things to say on the spot. For whatever reason, and I'm conviced of this, certain conversations are made worse by having the face to face element. It's easy to say things without thinking things through. Not to mention, it makes things that should be simple to resolve take forever to do so. It's too easy to see the other one upset and play off that emotion rather than focussing on carrying out the conversation that needs to be had. Some of the biggest hurdles in my relationship were settled in 5-10 text messages. It's fantastic honestly. We both say what we have to say and it's done with.
So I ask the question, are we going to reach a point where ending a relationship with technology becomes just as normal as starting one with it? I think so, and I don't necessarily think that's the worst thing in the world.