Shouldn't it be "cxu mi invitus vin al la balo" in stead of "invitu"?
-u is used when there is some kind of "pressure" to do something.
-us is used when speaking hypothetically, or contrary to fact.
With -us it would mean "Would I invite you to the ball?"
Could it be "should"?
No. "Should" contains the idea of obligation or pressure to do something. That would be the -u ending or "devus" depending on context. The ending -us is usually plain and simply... well, I already said it above.
No, I meant dnaleor's comment, for the actual question, would it be, "may I?" and "shall I" -invitos (technically)
Are you asking whether the OP could be "should"? I suppose so. Most native English speakers (Americans anyway) don't make a fine distinction between "shall" and "should" in day to day conversation.