Screening theory: Bundling problem
Consider the incentive and participation constraints. That is, look at which buyer types would choose which option.

A buyer does not buy anything if 
$$v_a &lt; p_a \quad v_b &lt; p_b \quad v_a +v_b &lt; p_{ab}.$$
A buyer chooses only good $i \in \{a,b\}$ with $j\neq i$ if
$$v_i - p_i \geq 0 \quad v_i - p_i \geq v_i + v_j - p_{ab}.$$
Otherwise she chooses the bundle.
With the assumption of independent uniformly distributed values, it then requires some caution to derive the probabilities of each event.

Finally, you want to maximize your profit given by
\begin{align}
(1-p_a)(p_{ab}-p_a) p_a + (1-p_b)(p_{ab}-p_b) p_b + \\
\left( \frac{(p_a + p_b - p_{ab})^2}{2} + (1 - p_a) (1 + p_a - p_{ab}) + (1 - p_b) (1 + p_b - p_{ab}) \\
- (1 - p_a) (1 - p_b) \right) p_{ab},
\end{align}
which is super annoying, but Mathematica suggests that your solution is correct.