Step 1: Understand the question.
The characteristic is the whole-number part of a common logarithm (base 10). We need the characteristic of the logarithm of the number 0.99.
Step 2: Recall the rule for numbers less than 1.
For a number smaller than 1, the characteristic is negative. It equals one more than the number of zeros that come right after the decimal point before the first non-zero digit.
Step 3: Count the zeros in 0.99.
In 0.99 the first digit after the decimal point is 9, not zero. So the number of leading zeros is $n = 0$.
Step 4: Apply the rule.
Characteristic $= -(n + 1) = -(0 + 1) = -1$.
Step 5: Make sense of the answer.
Since 0.99 is just below 1, its log is a small negative number, and its whole-number part written in bar form is $\bar{1}$, which means $-1$.
Step 6: Check the options and conclude.
The values 0, 1 and 2 are for numbers equal to or larger than 1, so they do not fit. The correct characteristic is -1.
\[ \boxed{\text{-1}} \]