Water the shrubs once a week during the first year after planting, providing 1 to 2 inches of water or enough to moisten the the soil throughout the root zone. Once established, banana shrubs are drought-tolerant and rarely require watering.
Spread a 2-inch layer of mulch over the soil, pulling it back so it doesn't rest against the lower stems of the shrub. Mulch helps retain moisture and prevents weed growth.
Prune the banana shrub after it finishes its main flush of blooming in early summer. Cut back dead or damaged stems to the nearest healthy wood, making the cuts within 1/4 inch of a leaf or bud. Cut back the remaining branches to the desired length, removing no more than one-half the shrub's height during pruning.
Monitor the shrub for leaf scale, which forms as white specks on the foliage of the banana shrub. Place a 2 tablespoons of neem oil in 1 gallon of water in a spray bottle and shake to mix. Spray the affected leaves until they are thoroughly coated. Repeat the application at seven-day intervals for a total of five applications.