Bul(l)rush is a puzzlement. The name has been applied to a variety of plants, including cattails or reedmace (Typha) as well as sedges (Scirpus) and rushes. Of course, in the Irish 17th century song, it was the laurel, no relation to any of these.
Wasn't a pharoah or some baby found in the bulrushes?
We will never know which plant it was.

Changing the subject to a question I have asked before, there is a modern song version copyright by Fred Brooks; "Green Grow the Lilacs," obviously a remake of the traditional song. According to Contemplator, it was sung by Texas cowboys, and was based on the 17th century Scottish "Green Grows the Laurel" which gets us back to "Green Grow the Rushes." (See previous thread, 46273, clickie above)
Still looking for the version that changes "red, white and blue," etc., to "Oregon Trail." My grandfather said he sang it (Colorado) when he was young (1880s-1890s). Don't remember his words, my memory got too oldt too soon.