Is it a bad idea to grow climbing vine plants like jasmine alongside bamboo?

I have some mature old hamii bamboo growing alongside my fence and I want to plan some kind of climbing vine to cover the fence and provide more privacy. I live in L.A. and so most things will grow well here but I don't want the vine to choke out the bamboo. Any thoughts on what would be a good vine to climb up a typical black wrought iron fence....about 6 feet high?