A true bolognese sauce doesn't require alcohol in any form. In our crazy mixed up american world things like bolognese get confused with pasta all' vodka. Strange but true. Milk in a bolognese is intended to offset the acidity of the small amount of tomatoes which are a key component.

I'd second VVV's suggestion, if indeed it's winefree you're looking for. Also, as the meat begins to lose its color, add a little milk and let it cook off. That adds some tenderness. A lesson learned from Marcella Hazan's books.

so i just peeked at your profile and think that maybe that question was supposed to say "without the alcohol." if that's the case, i'd suggest that you try adding a tablespoon of a hearty balsamic or red wine vinegar (red wine vinegar isn't alcoholic) to the sauce, along with some extra rich stock (chicken, beef, or veal) to make up for the amount of liquid you would otherwise use.

there are plenty of recipes that require very little or no wine at all, such as this one:
http://www.food.com/recipe/mario-batalis-fettuccine-bolognese-30991

if you have the hard rind from a piece of parmesan cheese, don't forget to add that in while the sauce simmers to add more depth of flavor-- just don't forget to take it out!

Try this recipe: http://www.food52.com/recipes/164_pink_bolognese
There are also quite a few bolognese recipes on epicurious.com and foodnetwork.com. Most add white wine with other liquid ingredients after browning the meat, then simmer.