I noticed that while watching a lot of footage of atomic & nuclear bomb
testing which took place during the cold-war era, virtually every time
a bomb was exploded there always seemed to be several vertical smoke
trails or columns which were close to the area of the blast; usually
slightly off to the sides. They looked similar to smoke trails that
are left behind by missiles, but there were always quite a few of them
spaced quite evenly apart from each other and there was never any
visual evidence that rockets or missiles had been launched straight up
to cause these vertical smoke lines. Besides that, the smoke trails
were not at all visible the moment before the bright light of the
explosion and then suddenly they are all there after the camera
adjusts to the proper exposure to capture the blast. This leads me to
believe that they may be caused by the nuclear bomb itself.

If this is in fact the case then my question is this. What are the
vertical smoke trails caused by? Or, if they aren't caused directly by
the bomb as a side-effect, what are they caused by and for what
purpose/why are they there?

Rockets were launched just before the detonation to leave smoke trails
that could be used to measure the shock front from the blast.

http://nuclearweaponarchive.org/Usa/Tests/SmokeTrails.html