Winter and Spring are the best times for pruning and cleaning out your bamboo clump. The stems that were produced in Autumn would have become hard, reducing the risk of losing the stem when cut, and the new shoots will have yet to emerge from the ground, depending on the species.
You can cut the plant anywhere, without hurting it, although it is best to choose a spot just above a node. Once the plant material is cut away, the part of the stem above the node will die back to the node. This can be unsightly if it is a long piece of stem. The nodal area is where the branches, then leaves grow from.
For the smaller more delicate varieties, you will only require a pair of secateurs and/or loppers to maintain your clump. Select the older stems and remove them at ground level. These will be the smaller, thinner stems closest to the centre, that are fully set with their foliage. It may be necessary to cut a path into that area of the clump to gain access.
If you desire a less open look, then only cut the upper parts of each stem that is leaning out. Or you can choose a number of the taller stems, and cut them down in height to force growth out from the lower nodes of those stems. This will create a low thick foliage screen, without reducing the height. The same principle applies for the larger varieties, although bigger equipment will be required.
Spring is also the best time to fertilise. There are many good products on the market. Always look for something that is properly formulated and is high in the N (Nitrogen) element. At least 10% or more. Fertilise under the mulch, then water in thoroughly. The foliage that has been removed during the pruning process, can be arranged at the base of the clump to be used as mulch if desired.