Is hedera helix, or common ivy, a bryophyte?

There are two types of land plants. Vascular and non-vascular. Vascular plants have xylem and phloem, non-vasculars do not. Nonvasculars are liverworts, hornworts, and moss, the bryophytes.  Does ivy have xylem and phloem? If so, then it's not a bryophyte (aka The Mosses).

Any plant with either a stem, roots, leaves, or any combination of the above is going to have evolved from a plant that had xylem and phloem. Vascular tissue came first.

Knowing this, and knowing what you do about the structure of ivy, you should be able to identify it as a bryophyte or not pretty easily. Bryophytes were the first land plants, and are the most primitive.