I think a rules lawyer could make a solid case for true strike's bonus carrying through to the bonus attack, but I think that this is a pretty clear case of 'letter of the law' not 'spirit of the law'.
I think the 'spirit of the law' is 'using the same base attack bonus', and that situational modifiers can change between the trip and the follow up attack (for instance obviously that the target is prone). Similarly, the situational modifier '+20 insight bonus' from true strike should be going away on the 'spirit of the law' rule that true stike only works for one roll of the die.
But in terms of 'letter of the law', I don't see any way to interpret it but treat True strike as if it was not expended in the attack. But, if some player tried to pull this trick on me, I'd immediately rule that Improved Trip has _no net effect_ (destroying the feat), since the target is obviously still standing _if the trip attack did not in fact happen_.
I hate rules lawyers.