Fencing is one way to banish unwanted pests from the garden. Chicken wire protects plants from nibbling of rabbits. For rabbit problems, 36 inches high is the best choice and should go approximately 6 inches below the soil surface. This is an easy, fairly inexpensive addition to the garden and is normally very effective. Another option is the electric fence, which does have to be buried to work well. A liquid fence is a spray-on, biodegradable product that is applied to the perimeter of the garden. It is nontoxic to pets or children but needs reapplication after it rains.
A number of natural repellants work. Chili powder spread in a circle around plants will deter rabbits from the garden. The pepper irritates the animal's nose and whiskers and deters nibbling on bamboo and other plants. The smell of blood meal sprinkled around the outside of the garden will deter rabbits. These also need reapplication after wet or windy weather.
For small populations of rabbits, humane trapping is simple and inexpensive. Humane traps won't hurt the animal, so they can be released into an environment similar to the garden but somewhere they won't be a nuisance.
If fencing and deterrents aren't enough, a number of plants will naturally repel rabbits and resist damage. Planting these along with bamboo will protect the bamboo and anything else inside the garden. The common boxwood (Buxus sempervirens), common barberry (Berberis vulgaris), lilac (Syringa) and spirea (Spiraea densiflors) each have tastes and smells that repel rabbits. Hydrangeas, daffodils (Narcissus), autumn crocus (Colchicum) and columbine (Aguilegia) are all flower species with properties that make them unappealing to rabbits.