I was induced at 38 (almost 39) weeks with my 2nd child.
We lived over an hour from the hospital, and my first labor only took 5 hours from the first contraction to delivery. My OB was terrified I would not make it to the hospital in time if I started labor on my own. And he probably was right, because once they started the pitocin drip on me, Jordan came in little over an hour!
But the thing about trying to make yourslef dilate, is that sometimes it can backfire. If the body is not ready, then the tissues will swell, and actually make the dilation shrink - it's not necessarily that the cervix itslef has closed down, but that the surrounding tissue has done so - but the same outcome.
There are topical medications that can cause the cervix to soften, but I believe they have the same components as pitocin, so Dr.s won't use them until actually ready to induce.