If I'm understanding you correctly, you're simply installing a French drain outside the barrier and not doing anything inside the barrier...right? If so the bamboo will have no more tendency to escape after you add the drain than before. With a 30" barrier, it's highly unlikely to dive down that deep under any circumstances. It will not somehow sense that you have a French drain and make a run for it.

Now that I re-read your title for your posting, I'm not sure exactly how you are going to construct this drain...or if I gave you a correct answer. Does the French drain get put on only one side of the barrier? Or are you going to run the bottom of the drain under the intact barrier? Or are you going to put the French drain on both sides of the barrier, but not penetrate it? Or what? Sorry, to be so dense, but between your title and the actual posting I'm just not envisioning exactly how this will run.

I plan on digging a approximate 48" vertical hole with a post-hole digger and filling it with coarse gravel. I will do this inside of my bamboo barrier with my growing bamboo. I hope that is clear. I plan on installing a vertical french drain inside of my barrier along with my running bamboo. If this is not a good idea I will not do it.

Thanks for clarifying. I can't make an absolute guarantee, but my view is that the rhizomes are just as unlikely to go that far down through gravel as through soil. I've never encountered rhizomes more than about 18" down. If it were me, I'd be ok with the idea. Good luck.