To upgrade you have to buy an eligible fare. The only eligible fares for 10k milesage upgrades are usually full-Y fares, which will often run more than the cheapest paid-business-class fares, so be sure to check those, too.

Once you have an eligible fare, you have to hope that there is upgrade inventory available (just because a seat can be purchased in business class doesn't mean you can upgrade into it with miles--they control inventory very tightly).

Bottom line: pick up the phone and call CO. Tell them what flights you want and see if there's upgrade inventory and how much it will cost.