White Bush Honeysuckle
Lonicera albiflora var. albiflora

This non-invasive viney shrub has white flowers in the spring. Plant in full sun.  It does not need a trellis and is drought tolerant once established. The fruit is red and hangs on during the winter.  In good conditions it will grow 4 to 5 feet.  In the Hill Country it is found on fence rows and hillsides.