I have 4 or so miniature hybrid roses in various stages of growth. They all are too young to produce ''wood'' yet. Most miniature roses sold are rooted cuttings, growing on their own roots. Most garden centers selling the larger rose types, hybrid teas, floribunda, climbing roses are grafted onto one understock or another. The understock is usually a wild type rose that blooms only once per year, late spring.
When buying a rose for bonsai there are a handful of nurseries, usually mail order only that sell the other types as own root roses. These are better for bonsai.
Shrub type roses more often than not are on their own roots.
Best types of roses for bonsai are probably the miniatures, especially for kusamono, the floribundas, and the shrub rose types. Pay attention to comments about disease resistance. Some hybrid teas in particular are very prone to leaf diseases, powdery mildew can be lethal. Black leaf spot is another big issue. The shrub types tend to be more resistant.
Depending what you want, be sure to note whether the rose is continuous, repeat or once blooming. The species types tend to bloom only once per year. Also note fragrance. To my mind, a rose that does not smell like a rose is not worth growing.
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