How do I move past my feelings for someone who doesn't feel the same way about me?

That is tough. Often it is hard to keep these things to being just physical and no emotional components to them because human beings have emotions, we tie emotions to things, it is a big part of how we create attachments to others. 

The best thing that I can tell you is in order to get past her, is to sever the ties. You will not be able to move on from the relationship, or the one you have in your mind that you want, until you cut ties and allow yourself to heal. You took the first step already and admitted to yourself that you do have feelings. You will need to sever the physical relationship with her. End the romantic piece, separate yourself from the friendship part for a period of time as well. She likely will be preoccupied in her new relationship for some time and it will not affect her as much.

You will need to fill your time spending time with others, go out with other friends, look for other romantic interests, perhaps look to online date or other ways of dating to find another romantic interest, find other hobbies and things you enjoy.  When you are at work, distract yourself with work, and try not to engage as much with her. Be professional and polite if you have to engage, but beyond that, separate yourself to make it clear that the relationship that she chose was a different one, you are not a disposable toy, and you are moving forward.  If you allow someone to treat you as though you are disposable, which in a sense is what has happened here, whether you initially agreed to the arrangement or not, they will continue to view you as that. Who knows if her relationship will work out or not, but you don't want to be the person at the other end that is just disposed of and picked up every time something goes wrong.  

The best way to get over a relationship is to fully end it for a period of time, until you are able to heal from it.  Once that has happened and you are able to have moved on, perhaps even have found a new relationship yourself, but are happy and over the situation, then maybe you can be friends again on some level, but not when one of you has feelings for the other.