People shouldn't have sex until and unless they're prepared to live with the possible consequences. Of course, those include pregnancy, STDs, etc.
I'm all for good and thorough sex education--which to my mind includes the above advice. And for doing what we can to limit unwanted pregnancies and abortions.
This bill? I haven't read it, but from the article I'd say it's not ideal but not entirely horrible. Doctors don't like it because they don't want anyone telling them what to do. And because it seems to increase their risk of being sued. Abortion advocates don't like it because its requirements tend to compel the physician and patient to recognize the fetus as a living human creature (person to many).
As usual, the whole argument hinges on whether or not you view the fetus as a (very vulnerable) person deserving of protection. If you do, then the rights to convenience or privacy of others becomes less important. If not, etc.
I do appreciate that there's a hypocrisy evident in those opposing governmental assurance of basic health care (etc.) and opposing (by government) easy access to abortion. No, preventing the destruction of life (if you can) isn't exactly the same as caring for life. But these two categories are not disparate, IMO.