Answer: Lonicera sempervirens (Trumpet honeysuckle) is a vining plant and will happily grow up a trellis or other support. It can reach ten or twenty feet if need be to match the size of the support. If there is no support for it to clamber on, it will mound up on itself in a self-supporting tangle. In my experience it is more attractive grown as a vine; the flowers are beautiful and last for a long season. If it surpasses its space simply cut it back after the first big flush of bloom. (Trimming in fall or early spring will remove most of the coming year's flowers.)
There are many species of honeysuckle, and some are actually bushes. The bushes are very sturdy and easy to grow, but tend to be somewhat large and inelegant and are best suited to shrub borders or wildlife habitat plantings. The bushes bloom once in spring and then form berries attractive to birds; in some areas however self-sown Amur honeysuckle bushes ( Lonicera maackii -- often seen for sale) have actually become a weed.
I suppose the answer to your question really depends on whether you have room for a bush or for a vine and how important the floral display is.
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