Use roughly five mimosa plants for every 200 square feet of exposed soil at the base of your bamboo plants. According to the University of Florida, this many plants should colonize and cover the area within one season. If you want denser coverage more quickly, use a few more plants.
Plant the mimosa plants at intervals of roughly 2 feet from one another and at least a foot out from the base of a bamboo stand where the soil is less dense with bamboo roots. This will allow a fairly rapid fill-in without causing problematic overcrowding of roots in the soil once the plants knit in and form a mat of foliage.
Cover the bare areas between the new mimosa plants with a thick layer of mulch. This will keep weeds at bay until the mimosa grows in completely and also help hold moisture in the soil which is crucial for the transplants.
Water the mimosa plants deeply immediately after planting, so that the root mass and soil around each plant is thoroughly wet.
Monitor soil moisture carefully as mimosa needs consistently and evenly moist soil until it is established and its tap roots can go deeper in the soil for water. Mimosa will also be competing with the bamboo for water so provide enough to keep both happy and free from wilt.