If your program does not offer any resources or assistance in finding an internship, seek one out on your own. Internships or any other type of supervised work experience in ornamental horticulture can lead to employment or better job prospects and recommendations.
If you're interested in research or teaching at the college level, you should pursue graduate work in a larger related field. For instance, if you wanted to study diseases that plague herbaceous plants, you could study plant pathology at the graduate level and concentrate in ornamental horticulture. Similarly, if you wanted to study ways to change the genes of a certain type of ornamental shrub, you could study plant science at the graduate level to do so.