To find out how much area Annie has to plant herbs, we first need to calculate the total area of the square garden bed.
The area \( A \) of a square is calculated using the formula:
\[
A = \text{side} \times \text{side}
\]
In this case, the side of the garden bed is 2.8 meters:
\[
A = 2.8 \, \text{m} \times 2.8 \, \text{m} = 7.84 \, \text{m}^2
\]
Annie is using one-quarter of the bed for tomatoes, so we can find the area allocated for tomatoes:
\[
\text{Area for tomatoes} = \frac{1}{4} \times 7.84 \, \text{m}^2 = 1.96 \, \text{m}^2
\]
Now, to find the area available for herbs, we subtract the area for tomatoes from the total area:
\[
\text{Area for herbs} = 7.84 \, \text{m}^2 - 1.96 \, \text{m}^2 = 5.88 \, \text{m}^2
\]
Therefore, the area Annie has to plant herbs is:
\[
\boxed{5.88 \, \text{square meters}}
\]
So the answer is **D. 5.88 square meters**.