I know that when you two hand a greatsword you get 1.5 str to damage. Say for some reason, somehow you have 6 str, for a -2 bonus. 1.5 x -2 is -3, So are you doing 2d6 -3 damage for two handing that?
The line just says apply 1 1/2 the character's strength bonus to damage, and it doesn't mention it being optional; it would seem that a character with 6 strength actually does less damage when two-handing a longsword versus swinging it in one hand.
It'd be as silly as arguing that someone with dexterity 5 has their AC go up when faced with a situation that causes you to "lose dexterity bonus to AC."