An accidental applies only through the current bar. You don't need to
apply a natural in subsequent bars. It just reverts back to natural.
In very chromatic music, it's not uncommon to put extra accidentals in
parentheses--(b), (#)--if there might be confusion. At least, that's in
classical notation.
In jazz, the rules are not so hard and fast. I'd be inclined to indicate
whatever accidentals and naturals I think will help the musician read
the music easily. But, I have never seen an accidental apply to more
than one bar, unless the altered note is tied across the bar line. Even
then, if the same note appears later in the second measure, it's assumed
to be natural.
Remember, though, jazz notation is a language of convenience. A good
jazz score will break all the "rules" of enharmonics, rhythmic notation,
and accidentals if it means you can read down the chart that much
easier.
HP