Kill them with kindness, be nice to them, praise them for jobs well done or for looking good. Their bitchiness will melt away and eventually they will be talking about how great you are and forget that they are competing with you.
If you fight them, you lose power.
I know exactly how you feel, so here's what I do! I do my work the best I can, I NEVER socialize with her & I keep my side clean so nobody can point fingers in my direction. Ignore them, usually if you ignore someone like this long enough, they will get the picture.
I hate to sound brutal but you may have to decide to toughen up a bit. Just think - by being sensitive in this scenario you are the only one who is suffering - they certainly aren't! Just try to develop a thicker skin at work. This doen't mean you have to become a hard-nosed b*** in your personal life, just create strong boundaries and don't let these awful people harm another moment of your precious life! Good luck...
Are they really bitchy and competitive, or are you a little OVER sensitive and emotional? It's a harsh fact, but true that sometimes we just have to toughen up a bit. Nobody should put up with being bullied, but you can't expect the world to be pink and fluffy all the time! ;0)