Tension will build, as Bridger will naturally be drawn in by curiosity, compassion and just perhaps, huba-huba! Louise Baltimore.
But Hudson will tend to be increasingly conservative, suspicious, cautious, authoritarian and restraining, asserting security concerns first. And, thanks to time travel, Hudson and Baltimore have a past. Even if, perhaps for Louise Baltimore, it hasn't happened yet!
And so, every time that Bridger will seek to advance the plot, Hudson must obstruct or discourages Bridger. But every time that Bridger is allowed go ahead, there may be dire consequences to prove Hudson right!
Likewise, Hudson will have an agenda that will seem cynical to Bridger, who will seek to moderate and restrain Hudson from doing something terrible advancing the plot in another darker direction.
Thus, Hudson and Bridger have really good personal, ideological and practical reasons to oppose one another, not just shallow bickering. And that is the sort of thing that will help provide dramatic conflict, essential to compelling fiction.
