This is where I get my Featherweight stuff. I have ordered their bobbins and have had no problems at all with them.
http://www.221parts.com/#
Also, before you get new bobbins, I'd really give that little machine a good cleaning. Remove the bobbin plate and really clean - use a flashlight so you can see really good to make sure there are no threads caught in there. Since the thread broke when it started skipping stitches, I'd bet there is something caught in there. After you clean under the slide plate and oil, turn the machine over, remove the bottom cover and clean and oil (there are like 13 oiling points under the machine) there really well - with a flashlight - so you can make sure nothing is wrapped around in or near the bobbin hook/race.
You should also take off the front face plate and oil every little hole in there that is suppose to be oiled - your book will show you where to oil. There are little oil holes to all the joints - something like 11 oil places altogother. You need to oil all the outside points too on the machine head itself. Since, you have re-threaded, changed needles, I bet it is not your bobbin at all - but, gunk or a thread somewhere that is messing up your stitch.
Good luck - let us know if you get it fixed.
Nancy