You can apply at the end of your third year and still write a senior thesis. It doesn't have to be either/or. If you want the entire thesis experience on your application, though, I guess you will have to apply at the end of your fourth year and take a year off.
I would strongly suggest writing a thesis. I wrote one and it was actually a lot of fun. It gives you a chance to pursue some original ideas, it looks really good on a resume, and it is not as challenging as it sounds.