I'll be starting bouncing at around 37 weeks since I'm still at risk to go into labor at any time. Don't want to feel guilty for doing anything until I at least am considered at a safer point. Anyhow, I don't really think that bouncing or any other measures work on actually starting labor. I just think they help prepare your body for it. As for bouncing on a ball, it just helps start the engagement process. Hip circles are GREAT for helping open up the pelvis. So do those if you can. I have tiny hips so I'll be doing that a lot.
As for the hospital having birth balls.Some do and some don't. It's always good to check with your midwife/doctor/whomever and see if your hospital has them. If they don't know call your labor ward and ask. My hospital offers two and has about 20 labor rooms (maybe more). So if I go in and the ward is pretty full, even if there are 5 women in there the chances of having a ball available is pretty low. I plan on stuffing our pumped one in the back seat and taking it in with me. I want to use it not only to labor on, but to use as a chair in the shower to help with pains (we don't have the option of birthing baths there). If you decide to do that, don't forget to put a towel underneath it so it doesn't slip!
I don't think so! My hospital has them but we're tiny (two delivery rooms to give you an idea of just how tiny) I've watched OBEM etc though and they all seem to have them 
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