my 10.5 US 16" bamboo needle (cheap brand) started to split and break during a pumpkin I was working on. I used a little electrical tape and was able to finish, and knit another item on them. I'm not sure if that trick would work if it broke completeley off though.
I don't know about fixing them, but just to reassure you-- yes, I also had a cheap bamboo circ break in the midst of a sweater. Fortunately, changing to another circ didn't alter the gauge (different materials used in the needles can do that), but I was none too happy, even though it was cheap!