By comparison with other versions, I strongly suspect that "Come be with me" is a mishearing of "Come fee with me", "fee" being the common term in Scotland (and NI?) for agreeing to work for a period (possibly six months) for payment. A version that I have encountered, where the man is addressed as "Tam Buie", has the woman not declaring herself a widow at first. When it gets to the offer of sharing her bed, the man asks what about her husband. She replies "Dead and gone". He asks how long the husband has been dead. The widow's reply can then be either "Seven long years" or, for added humour, "Seven long days".