Congratulations on your new home!* Often common names for plants can be misleading.* When you say you have umbrella bamboo I'm thinking you are talking about Fargesia murielae.
This is a clump forming bamboo and the culms grow facing outward.* You should be able to just dig out the clumps.* I would suggest you cut the canes near the ground first.* If you live near a zoo that has pandas you might consider donating the canes to them as these are an important food for the giant panda.
In the US there are a total of 11 giant pandas.* They are at the Smithsonian National Zoological Park in Washington, D.C., Zoo Atlanta in Georgia, the Memphis Zoo in Tennessee, and southern California's San Diego Zoo.
When weeding, the best way to make sure you are removing a weed and not a valuable plant is to pull on it. If it comes out of the ground easily, it is a valuable plant.