RAW, the base price of the bow would be the only adjusted price. The write up basically says increase the price of the (base) bow by X per STR mod.
I don't think the rules specify this either way, but common sense tells us you double the price/cost of large weapons because more materials are used to create them and more time/craftsmanship is needed to make them. It only seems logical that composite bows are made of special materials and a great deal of craftsmanship is needed to make one. Making a high-STR composite bow costs even more because it needs even more special materials and more time and effort to make it. Making one twice as big seems like it needs still more of the extra-special materials and even more time, therefore, the multiplier seems to apply to the whole price, not just to the base price before STR is factored in.
You might wanna x4 the cost, at least, as a doubling in length is a x4 mulitiplier in mass of the item.
If Pathfinder obeyed the square/cube law, it'd be a hell of a boring game.
The size write up says a large weapon costs twice the listed price. Again, regardles of what would seem to make sense, RAW is the base price being doubled. Then the write up of composite bow would modify the doubled listed price.