You can't upgrade on ANA flights or any other code share flights to Asia using miles unless you by a Y/B..or perhaps other fare but it's waaay up there (full or near full fare economy) and do a Star Alliance upgrade and that is going to cost a fortune. UA does not fly to BKK any longer... so the only way you're going to be able to do this on the cheapest fare using miles is to fly on UA to NRT, HKG, or SIN and then get a connecting flight on another airline in economy for the shorter flight(s). If you want it to be a one stop from LAX with United as your long haul carrier (with a shot at upgrading)..then NRT is the only connection option. On the cheapest fare there will also be a $600 copay each way on United on top of the miles (I believe 30,000 miles each way). If you book a higher economy booking code such as M, H, Q, V, W it will get you a lower copay...(look at the upgrade award chart at United.com). It also might improve your chance at an upgrade, but it often will cost more to buy than the $ you'll save in the reduced copay, and you won't get any refund of the higher fare if your upgrade doesn't clear. If your upgrade doesn't clear you'll be refunded the miles and the copay (both of which you have to pay when the upgrade is requested).

Getting a free award ticket in business or first class is far cheaper in terms of $$, but finding space far out is often hard to do. Close in though you might have luck.