This is not an easy situation as I'm sure you know. Is this colony isolated in your yard or has it broached neighboring properties? Either way it will need to be controlled in all areas to attempt to eradicate it, or it will continue to come back from the areas no treated.

Here are the options as I see it. #1 kill all of the bamboo. #2 create a physical barrier in the soil to prevent the rhizomes (underground stems) from penetrating into areas you want to eradicate it. This would also apply if say your neighbor has it and doesn't want to remove it, but you do. #3 is to treat what comes up every year to suppress it, knowing it will be a yearly battle.

If option #1 is possible, check out my information in option #3 and apply to all. All of the sources I have looked at suggest that it may take a couple years to completely get rid of the bamboo and that combined efforts including removing rhizomes, mowing, and multiple herbicide applications together may provide the most effective long-term control.

Option #2. For installing a barrier there are some good instructions and a video on this website from the University of Maryland.
https://extension.umd.edu/resource/containing-and-removing-bamboo

Option #3. If the plants around where the shoots are coming up are one that you don’t care about or could be replanted later then glyphosate (Roundup Super Concentrate) is probably the safest first option. This can be applied either as a direct application into the hollow space of cut stems (which may be most effective) or as a spray to the leaves (most likely to drift onto other plants).

When using products containing glyphosate there are a few important points to consider. First, as with any pesticide, remember to read and follow all labeled instructions. Second, glyphosate is a broad-spectrum herbicide, meaning it will injure or kill other plants contacted during application, so care is needed to avoid green plant material, exposed roots, and injured bark of desired plants. Third, glyphosate is relatively safe in the environment when used as labeled. It adsorbs strongly to soil in most cases (i.e. clay and organic matter), allowing even sensitive crops to be planted shortly after application; meaning no carryover issues are expected. Fourth, glyphosate alone can take up to 14 days to show full activity under ideal growing conditions. Retreatment of the area may be needed depending on the degree of infestation. Glyphosate is most effective for perennial control in the fall but can be applied anytime the plants are actively growing (temperatures consistently above 50F). For woody species, periods of heavy sap flow in the spring may not be effective times to treat. Finally, be sure that the product you choose has only the active ingredient glyphosate or glyphosate + pelargonic acid. Products with additional active ingredients may have other unwanted effects and may delay the planting of other plants in the coming season(s).

The Roundup.com website does have some information that might be useful about applying glyphosate to cut bamboo stems.
https://www.roundup.com/en-us/library/specific-weeds/what-bamboo-and-how-do-i-control-it

There is a more potent option, but only for bareground areas where you desire no vegetation…Another active ingredient that has been shown to be more effective in controlling bamboo is imazapyr. This can be found in combination with glyphosate in the product by Ragan & Massey called RM43 Total Vegetation Control (available at TSC, there may be other products as well). You can also find imazapyr in Ortho Groundclear Year Long Vegetation Killer (imazapyr + pelargonic acid), but I'm not sure if the pelargonic acid might cause some antagonism (i.e. reduced efficacy). These products will prevent the germination of anything new you plant for a year or more (according to the label, usually more if it is a clay soil). These products can also cause damage to desirable trees and shrubs if applied over the root system.

I hope this helps. Please let me know if you have any additional questions.