First off, good question. That always bothered me a bit as well.

I think we'll get more information on her motivation, both from Mat's POV (once he opens the letter), and possibly from Egwene (decoding the book), or someone else who received a visit/letter from Verin.

In terms of Mat's letter, two thoughts. There are two plausible interpretations of the Verin/Mat agreement.

First, Mat has two choices:
a) Wait at least 10 days before opening the letter, if he opens it, he has to do what it says, OR
b) Wait in Caemlyn for 30 days after she drops him off.

Under this scenario (which I think most believe), Mat can open the letter on day 11, or day 29, or even day 30. If so, then it is doubtful that Verin revealed any BA secrets to Mat, because then the deadline isn't hard and fast. She could have simply checked in on him to see if he'd opened it yet before killing herself, but she didn't.

Second option, Mat can:
a) Open the letter ON day 10 (wait 10 days AND open the letter), OR
b) Wait 30 days in Caemlyn.

If you re-read tGS and the interchange between them, I think this is the much more correct interpretation of the agreement. If so, then I think there is a much better chance that Verin betrayed her oaths in her letter to Mat. Therefore, she only had 10 days to act and couldn't wait any longer.

Now, there could be some other reason that we find out why she couldn't wait (maybe she had foreknowledge of the Seanchan attack, or more pressing info to give to another letter recipient), but I think the second scenario is the more likely one.