Here is what I have heard.
- Once you cut it down wait on new growth.
- Try weed killer on those fresh new shoots.
- Cut down the ones that survive for any length of time
- Repeat the weed killer on the new groth.
- Repeat until it is done.
- Others here may give you better advice.
AND...
- Not all bamboo runs. Research Clumping bamboo.
- Your barrier for runners should be a two or three feet down and a few inches (2 to 4 maybe) above ground.
- Google Bamboo Barriers
- Armed with information bamboo becomes a very interesting subject and can be an asset to any garden.

Hope this helps.

How sure are you that it is bamboo? There are several invasive plants that sort of look like bamboo (Japanese knotweed, Arundo donax, etc.) to the uninformed eye. These are usually much harder to get rid of than bamboo, and, despite what you may have heard about bamboo, it's not as invasive as you're describing. The answer to your question depends on what it is. So how do you know it's bamboo, other than that's what someone told you? If you're not 100% convinced it's bamboo, a picture would be useful.

To control bamboo, you need to rhizome prune at least once a year, using a shovel to discover and sever the rhizomes that are going where you don't want them. Unlike many plants, severing the rhizomes kills all growth beyond the cut line...as long as you haven't let the rhizomes do their own thing for a couple of years and establish new "satellites." If the rhizomes you went after were fairly recent growth, you would not have had to remove any of your patio; you just would have had to cut the rhizomes at the edge where they went under the patio. However, it's not clear whether yours are established or not. And I'll repeat from my previous message, stuff like Roundup generally doesn't seem to help much.
And I guarantee that the stock clerk at HD is not the best source for specialized gardening info.

Beth-
Please ignore my second posting...I was answering a question for another posting and somehow plunked it down here. As for my first posting right before that, I'm still curious if it's really bamboo.

Kudzu, I looked up both of the plants you might have thought I had, and neither one of them matched -- this stuff is definitely bamboo.
But my question really is: will vegetation killer work? and if so, should I spray it on the leaves or on the runners underground? Or what other options do I have to stop the li'l sprouts from . . . sprouting? I need a set of pandas . ..

Beth-
There are other plants that resemble amboo...I just didn't list them all. However, I'll take your word for it that it's definitely bamboo. Vegetation killer typically does not work on bamboo, thought it does on other invasive plants. Typically you have two options. The first is to dig/pry it all out, which can be a lot of work. The second is to follow the advice of the ABS (American Bamboo Society), which will take a while to accomplish your goal. I'm still curious what you have. Is this something with a woody culm and separate leafy branches that extend from the culm, or are the leaves coming directly from the culm? And does it die back to the ground in winter?

Here is a link that might be useful: ABS - Control

Using herbicide to kill bamboo works best if you apply the herbicide in the late summer or fall when the sap is flowing back down into the rhizomes. Cut down the cane and immediately paint the stump with full strength Roundup. Then in the spring you'll have to cut out a few weak shoots that appear. My brother used this method to selectively kill out aureosulcata bamboo that had gotten intermixed into his moso bamboo grove without harming the moso.