To paint or not to paint?  That is the question!
 
Some books I have read insist that no surface that comes into direct
contact with the bees shall be painted.  This is the practice I followed
for over a decade and paid the price of bottom boards that did not stand
up to the elements and needed to be replaced after four or five years
use.  Reasons mentioned in the books were mainly due to the bees'
aversion to painted surfaces (especially oil based paints).
 
A few years back, I had a problem with foul brood.  After I purged by
fire, the State Bee Inspector (who also had 25 years of commercial
beekeeping under his belt) suggested that after I scorched the inside of
the hive bodies, that I give them a quick coat of paint.  I mentioned the
conflict between his advice and what I had read, to which he responded
"Poppycock!" or some other quaint colloquialism, and assured me that
with sufficient air-out time the inside painted surfaces would be fine.
I have since encountered inside painted surfaces with many years of
habitation by bees with no ill effect.
 
So, the short of it is go ahead, paint away.  Again, allow sufficient
time for your bottom board(s) to air out and avoid oil based paints as
they smell more offensively and take longer to air out.  In this day and
age it bewilders me why anyone would forsake latex for oil base anyway.