First, there's a difference between the teacher's union and teachers (just as all unions). Unions are generally partisan. Why? Because Republicans are anti-labor, hence anti-collective bargaining.
The actual teachers probably lean left, as they're educated (who generally tend to lean left), but as most teachers aren't actively part of collective bargaining (although benefit from it) it usually isn't part of their calculus. Things like abortion, gay marriage, gun rights, taxation, affirmitive action, and other issues like that are likely just as important to any individual teacher.
That table is fairly old, but even using that table, more people with bachelors or graduate degree lean left than right (3392 v 3278). Historically, those with degrees leaned right. It's been trending left and I wouldn't be surprised if this was the point where the lines crossed.
Here's more recent data (http://www.gallup.com/poll/118528/gop-losses-span-nearly-dem...), and as you can see Republicans have lost 10% of college grad support since 2001. As you can also see, in 2001 most with college grads slightly leaned Republican. By 2009 it is hugely slanted Democratic. This is consistent with my theory that the data you provided where college grads slightly lean left was one of the first years where the lines crossed and its been an exodus of college grads to the left ever since.
2009 was basically the low-water mark for the GOP brand in modern history, so I'm not sure that those numbers are all that accurate now, but it's not a huge deal.
More to the point, the party gap in with college degrees is surely vastly smaller than the party gap in the private workforce vs members of public-sector unions, so it's sort of weird to assert that the reason teachers lean Democratic is that they're "more educated."
Edit: OK, I messed around with matplotlib and made a couple plots. This kind of data is not my specialty. The bottom plot groups the different Democratic and Republican categories into just Democratic and Republican.
The strongest trend seems to be that people in the "strong Republican" group increase with educational attainment. I made the (poor?) assumption that teachers are most likely to fall into the graduate degree category, thus the bottom plot.
The actual teachers probably lean left, as they're educated (who generally tend to lean left), but as most teachers aren't actively part of collective bargaining (although benefit from it) it usually isn't part of their calculus. Things like abortion, gay marriage, gun rights, taxation, affirmitive action, and other issues like that are likely just as important to any individual teacher.