ok I'm going to stick my bill in so to speak
first off I'm willing to be corrected on any of this I am not working from primary sources, I don't have copies of the original documents and can't read medieval latin/norman-french and middle english gives me a headache so I am relying on translations and reprouctions and apologise for any bastardisation that has occured without my knowledge.
bill, originally bil in old english meaning a cutting tool, hence why the term bill is so generic.
References to the "bill" in contemporary (very loose as the ones I have to hand at this juncture are some 400 years apart, but this does suggest that it was in use in some form throughout the medieval and into tudor period)
From Wace (12th century anglo norman poet/canon of Bayeux) and I admitt working from a translation whose accuracy I am taking on faith
"There was a French soldier of noble mien, who sat his horse gallantly. He spied two Englishmen who were also carrying themselves boldly. They were men of great worth and had become companions in arms, and fought togehter, the one protecting the other. They bore two long and broad bills, and did great mischief amongst the Normans, killing both horses and men..."
again from Wace, this time speaking about the battle of Hastings
"And now might be heard the loud clan and cry of battle, and the clashing of Lances. The English stood firm in their barricades, and shivered the lances, beating them into pieces with their bills"
1551, Daniel Barbaro Venetian Ambassador to the English court
[He first talks of archers and their ability to slaughter huge armies and then] "the second is of bill-men, their weapons being a short thick staff, with an iron [presumably refering to the blade] like a peasants hedging bil but much thicker and heavier than used in Venetian territories. With this they strike so violently as to unhorse the cavalry; and it is made short because they like close quarters"
Sir Roger Williams from "A Briefe Discourse of Warre" published 1590
"I persuade myself that there ought to be amongst 1000 pikes, 200 short weapons, as holberts or bills; but the Bills must bee of good stuffe, not like our common browne bills...." he goes on to talk at some length about steel rather than iron and how they should have strong pikes (presumably blades?) at least 12in long and langets to the middle of the shaft "like unto those the Earl of Leicester and Sir William Pelham had in the low countries for their guards"
In my opinion the greatest problem as regards bills and thereby billmen is what actually constituted a bill in the medieval sense. A bil as in a cutting tool is practically 90 odd percent of the close quarter weapons on a medieval battlefield. As with everything we do given the relative lack of evidence, compared with say Napoleonic or the World Wars, a certain amount of interpretaion of the evidence we do have will always be necessary. To my mind though a billman is a man armed with a jack, sallet (helmet) and stave (as per serviving muster rolls) whether that stave is a spear, boar spear, partisan, glaive, welsh hook, hedging/hand bill on a long stick or any other of the hundreds of designs seen in collections/finds etc
Billman is an acceptable term, simply in that it is the best term we have to describe a complex and varied infantry type.
Finally, I apologise for the 100 or so typos mispellings there probably are in this post, I'm tired and can't be bothered proof reading all that
Heads you live...tails you die.