Do i invite my supervisor to my wedding?

I think a good rule of thumb is to consider whether you’d hang out regularly outside of work. Would you go out for dinner or drinks with this person (or better yet would you pay for their drinks/dinner)? Or would you invite them to your birthday party?
Based on your description I’d guess the answer to those is no? Even though you’ll be spending a lot of time together you don’t know for sure you’ll develop a close friendship.
But if you feel your relationship is close enough to say yes to the above and your guest list has space then inviting her isn’t a bad idea. But if she won’t know anybody else there I think you should give a plus one even if you think she’ll get along with your other guests. It’s awkward not knowing anyone at an event like a wedding. If you aren’t willing to do that or there isn’t room for a plus one I’d say don't invite her.

If I was in your shoes, I wouldn't invite her. Even though you guys are somewhat close, you guys only work together. Do you see her outside of work and such? I'm very close to a couple of my co-workers but I'm not inviting them to my wedding. I get along with them super well but I don't see them outside of work and don't really talk to them outside of work either.