Rest assured, once you start the softening, it can be some time before full labor happens, just as njeosys said. And don't worry if you do go into labor around 37-38 weeks, it's a perfectly safe time to have your baby. My second one started labor at 34 weeks, and they put me off until 35, and although he only weighed 5lb. 8 oz., he's a healthy little man, and we had no issues with him. He'll be 4 in February. Good luck to you!!! (and try to relax a little :)
Your cervix is softening in preparation for labor. In other words, it is beginning to dilate (or open) and efface (thin out). You can be dilated at 3 cm for WEEKS before you actually go into real labor. The blood was probably just your mucous plug (some women bleed). Didn't they tell you anything at the hospital?! I am just amazed how doctors cannot keep a scared, pregnant woman informed.
So you probably won't go into full labor soon. I was dilated at 3 cm and 100% effaced with my first daughter for two weeks before I went into labor and had her (I was 2 days shy of her due date). A softening cervix is not a bad thing!
Just take it easy!