Annie has a square garden bed that measures 2.8 meters on each side, and she plans to fill it with tomatoes and herbs. She decides to use one-quarter of the bed for tomatoes and the rest for herbs.

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**.