I could give you examples of how NOT to do it, and I'm not sure there's an easy way to break up with someone. Thalia gives a good suggestion, though. I also like what you said at the end - simply "I'm sorry, but I'm just not ready for a relationship." That's it - nothing else. (It's tempting for women to want to say a lot more, but you probably don't need to.)
As for timing, I'd suggest doing it now. There will probably be some awkwardness, but if both of you approach your roles in the play as professionals (i.e., you're there to do a job, to entertain the audience, etc. not to be a couple) that might actually be a way to get through the awkwardness, and perhaps build some professional respect for each other. (Warning: the opposite could happen, too, if the two of you couldn't take the "be professional" route.) The first week or so is usually the worst, particularly since you guys see each other often. You just have to get through that part I'm afraid.