You can use ^
(exclusive or) to flip a bit. For example:
set @input = 15
set @bit = 4
set @result = @input ^ power(2, @bit - 1)
In a binary system, multiplying by two shifts all the bits one place to the left. So you can implement a 1-bit rotation by a shift and then manually carrying the top bit to the bottom bit:
set @input = 128
set @result =
case
when @input & 128 > 0 then (@input ^ 128) * 2 + 1
else @input * 2
end