I don't know what to say or how to say it... or what to do. Please help!

There is someone that I cannot avoid who likes to sit across from me, but she is disgusting. She may not even know she has this problem. The problem is that she spits when she talks, plus she has a disgusting mouth so her spit is NASTY! It honestly makes me sick to sit across from her when she does that. (I'm not describing how bad this is because I don't want to make people reading this sick. Trust me, it's awful! I'm leaving details out.) And I feel like I can't eat when she's there doing that. Without going into too much detail, I am stuck sitting somewhere for hours and she tends to come and sit across from me. I would like for her to sit further away from me, but just don't know how to ask. If I do ask, she will ask why I ask.

How can I get her to get away. I don't dislike her. She is a sweet person and vulnerable and homeless... But I need for her to stop doing that.

What can I say to her?