And if you don't LIKE onions, as opposed to not HAVING onions, well, mince them up finely and cook them thoroughly. They blend into the sauce and are almost indistinguishable as a separate oniony bit, but still lend their marvelous flavor.

Bolognese uses a combination of meats; typically veal/beef and pork. It's one of the few Italian "sauces" that actually cooks for a long time. Begin with a "soffrito" of carrots, onions, celery and pancetta. Cook that down in butter, not oil. Add the meats, color that. Add a bit of white wine, canned tomato paste, milk. Thyme, salt and pepper. Chicken livers in the meat mixture would not be a bad thing. Please note that this is not "red sauce" or "gravy".

What else don't you have aside from onion? Use a few cloves of garlic. You need to always have onion in the house! If I have an onion, I can always cobble up a meal from odds and ends.

No. In order to make proper bolognese, or any decent ragu, you need to use the real ingredients.