To solve this problem, we need to understand the relationship between the number of straight lines and the bounded and unbounded regions they form.

Let's start by considering the case when there is only one straight line. In this case, there is only one bounded region and one unbounded region. So, B = 1 and U = 1.

Now, let's add a second straight line. The second line can intersect the first line or be parallel to it.

- If the second line intersects the first line, it creates one more bounded region and one more unbounded region. So, B = B + 1 and U = U + 1.
- If the second line is parallel to the first line, it does not create any new bounded region, but it splits the unbounded region into two. So, B remains the same and U = U + 1.

Now, let's add a third straight line. The third line can intersect the other two lines, be parallel to one of them, or be parallel to both.

- If the third line intersects the other two lines, it creates one more bounded region and one more unbounded region. So, B = B + 1 and U = U + 1.
- If the third line is parallel to one of the other lines, it does not create any new bounded region, but it splits the unbounded region into two. So, B remains the same and U = U + 1.
- If the third line is parallel to both of the other lines, it does not create any new bounded region and does not split the unbounded region. So, B remains the same and U remains the same.

We can continue this pattern for each additional line, considering all possible cases of intersection and parallel lines.

Now, let's consider the maximum possible number of bounded regions. When m straight lines are drawn in a plane, the maximum number of bounded regions they can form is given by the formula:

B = (m^2 + m + 2) / 2

For example, when m = 3, B = (3^2 + 3 + 2) / 2 = 28 / 2 = 14.

So, in this problem, we are given that B = 28. We need to find U, the maximum possible number of unbounded regions.

Using the formula for B, we can rearrange it to solve for m:

m^2 + m - 56 = 0

Solving this quadratic equation, we find that m = 7 or m = -8. Since the number of lines cannot be negative, we take m = 7.

Now, substituting m = 7 into the formula for B, we find that B = (7^2 + 7 + 2) / 2 = 28.

So, U = m + 1 - B = 7 + 1 - 28 = -20.

Since the number of unbounded regions cannot be negative, we take U = 0.

Therefore, the sum of U and B is 0 + 28 = 28.

Hence, the correct answer is option B.