I don't think there's anything wrong with offering to sit with somebody who's eating by themselves (although I myself do prefer to be left alone while I eat, too), but Jesus Christ fucking ask first it's not hard. "Hey, mind if I sit here?". See? Done. That's all it takes. 6 words. Just expect that you might get a no, and that that's okay. Also, don't ask after you've already sat down, or while you're half sitting already