Your code would be much faster if you didn't so many unnecessary conversions. a.a is a comma separated list (which is bascially a cell array) which you convert to a char array and then split back into a cell array.
output = contains({a.a}, 'b')
does the same without any conversion.
It's not clear from your simple example if you really want to use contains (which check that 'b' is present anywhere within the char vector) or strcmp (which check that the char vector is exactly identical to 'b') which would be faster or even == which would be even faster but only work if all char vectors are just one character.
output = strcmp({a.a}, 'b') %faster than contains if whole string comparison is required
Other than that, there's not much option to speed this up.
