I have to disagree with those who say go via Europe. From SFO, it's 9500 miles to go SFO-BKK-BLR, or 10500 miles to go SFO-FRA-BLR. It's 1000 fewer miles to go transpac.
Now, I also prefer transpac because I'm a UA flyer. I can upgrade all the way to BKK and a C ticket on TG isn't that much extra.
I agree with others who say that you should look to see where you can use your OneWorld Sapphire status to your advantage (no pun intended) or at least earn miles/status on AA. However, if you plan to make this trip often, you would be better off changing to UA and the * Alliance which better serves the market.
AA doesn't fly West of Japan, but you could perhaps fly BA from London to Mumbai or Chennai (they don't serve BLR last I checked). Again, it's an extra 1,000 miles, but if it's upgraded vs. coach then the choice is clear.