I would be polite but distant. If I really don't like someone, I would never be rude but I would not go out of my way to engage them in conversation. But sometimes it helps to figure out why you don't like someone to get peace with it.
Yes, I think that's going to their level, I think giving people the benefit of the doubt is a good thing, but sometimes that limit can be reached. Plus some people just have an attitude that never disappears.
If you have to be around the person every day, that sucks. You just have to establish boundaries in how you relate with the person. Know your non-negotiables and don't let the person cross them. By keeping a safe distance, you can prevent it from happening. Limit conversations and when you must, choose topics that aren't incendiary. When worse comes to worst, pretend you're asleep, if the situation allows you to.