To further address Jim C's post and Felipe's, "may" can be hawthorn:
it sure is in southern England [certainly as far north as Gloucestershire]. It's a likely local name for the main flower that blooms in May. If the spelling is accurate, surely "bonnie" suggests a Scots origin, hence the broom is the yellow flower, as in The Broom Of The Cowdenknowes. I'm less sure if that's Spring flower.