What is an example of an angiosperm with woody tissue?

apple tree.

Bamboo is woody rather than having wood.

Woody usually means wood-like but lacking the clear architecture of wood. The monocots with distributed vascular bundles (xylem & phloem) dotted about in the trunk in a regular pattern are what provide 'woody' structure.
The difference between monocots (woody) and dicots (wood) vascular architecture lies in their tissue cells being organized from different locations in the respective stems. They both have xylem and phloem, tissue cell types, but the tissue origin of these cells differs, dicots grow from the circumference, and monocots, like bamboo, from section ends. Dicots have lateral meristem, the cambium, as the source of their vascular tissue system. This results in only dicots having wood with lateral meristemic growth that adds annual girth to the plant. Monocots have intercalary meristem at the nodes (where the leaves attach). The intercalary meristems lengthen the plant, usually for a short time, and produce the discrete distribution pattern of their vascular tissue architecture.

A tulip tree.