A wheat cultivar, designated BZ6W07-458, is disclosed. The invention relates to the seeds, plants, and hybrids of wheat cultivar BZ6W07-458, and to methods for producing a wheat plant produced by crossing plants from wheat cultivar BZ6W07-458 with themselves or with plants from another wheat variety. The invention also relates to methods for producing a wheat plant containing in its genetic material one or more transgenes and to the transgenic wheat plants and plant parts produced by those methods. The invention also relates to wheat varieties or breeding varieties and plant parts derived from wheat cultivar BZ6W07-458, to methods for producing other wheat varieties, lines or plant parts derived from wheat cultivar BZ6W07-458, and to the wheat plants, varieties, and their parts derived from the use of those methods. The invention further relates to hybrid wheat seeds and plants produced by crossing wheat cultivar BZ6W07-458 with another wheat cultivar.