You probably have a ground-cover variety of bamboo, and those are harder to remove since you have so many more tiny rhizomes so it is basically like a lawn in itself. If it's not too big of an area, you might want to try digging it all out. You could also just treat it like grass, and mow it every week, and you'll just end up with a lawn that has extra large leaves. Since it grows just like a lawn, if you have a large dark plastic tarp, and put it over the bamboo, that should kill it off in a few months since it won't have a source of energy.

If you want to get the bamboo out without killing the grass, the only way is to pull all of the rhizomes out by hand. Most of the groundcover bamboos have rhizomes that don't go too deep, so this may not be too difficult. I'd suggest doing it when the ground is moist. You should be able to grab one end of a rhizome and pull a long section up out of the ground, but if they branch too much it may be impossible.

I agree that digging it out is the only thing that will work. I had a clump of groundcover bamboo that got too big on a hillside. The rhizomes were very thin (about 1/8" in diameter), were only several inches deep, and were not in amongst other plants or grass...but I still had to use a pickaxe to get them out and had to totally dig up the whole area. Even then, I had a couple of strays come up the next year from chunks of rhizome I had missed.

Unfortunately, I suspect that you will not be able to get the rhizomes out without pretty much destroying the lawn in that area.