It's been a while, but I'd imagine 4-40. A phone call to Paul would give you a definitive answer as opposed to taking advice from some clueless rando on the internet.

I'm puzzled. Didn't know Beard Resos had "machine screws" and inserts? What is the advantage?
How many time do folks remove or adjust the old...I think #4 wood screws holding the cover plate in place? If the wood screw gets loose...a simple fix is take a wood chip or tooth pick...glue it in the worn area and put the screw back into that location. Loctite medium strength will help with a repair as well. No criticism here...just curiosity...always trying to learn.
Be Well

A phone call to Paul would give you a definitive answer as opposed to taking advice from some clueless rando on the internet.

OK, That was totally uncalled for. I'm sorry.
Actually one of the more elegant design features of Beard guitars is the brass threaded inserts that are installed in the tops of the guitars to reduce the risk of stripping the holes with wood screws. A minor detail, for sure. But a great convenience if you are keeping and playing a guitar for a long period of time and maintaining it regularly. Makes removal of the coverplate an easy, worry free task.
Just another cool Beard innovation.

PM sent to dobrotome

I would just remove a bolt, take it to a hardware store, find a nut that fits it & then buy a bolt with that thread size that looks like what you brought. I’ve had to do this on Fender/Squier products before due to inconsistencies between American, Mexican & Indonesian made products (and differing opinions).

Top inserts have been a design feature in Beard guitars since (at least) 1986. (Beard #2)

For those that play a LOT and where the cone is subjected to normal elements many of us do complete tear downs of our axes 2-3 times/year to remediate cone oxidation, get rid of stubborn substances that effect cone response or do up close inspections of bridge inserts, pickups or other internal components.

If you're in that camp, that very last thing you want to be dealing with is a top repair, however minor.

Periodic preventive maintenance is a real thing for some of us and there's been many a time I've mentally thought, "thanks Paul"!

h

+1 HLP and kelfranken posts. Love threaded inserts - should be standard equipment on every reso.

Since nearly everything under the sun has been discussed here at one time or another regarding spider bridge resos in the hangout's 17 years of existence, I found one of my old posts on the subject and modified it a bit to bring it up to date:

As far as threaded inserts and machine screws like Paul uses - that one has struck me over the years as the greatest thing since sliced bread on dobros along with the removable palm rest. 

Not everyone agrees. At ResoSummit  in Nashville 15 years ago while taking Tim Scheerhorn's setup class I brought up the Beard threaded inserts and he sort of dismissed it with a frown and scoffed at the idea. 

He showed us how to correctly seat the screw on an old Dobro by very gently starting it counter clockwise before reversing the order to tighten it, and listen for a little click before screwing it into the hole. It's one of the few things I have in common with wizard Bobby Wright when it comes to setting up a dobro - we both learned this from Mr. Scheerhorn.

For badger who is a long-time pro cabinet maker this is probably Screw Techniques 101 material.

I just kind of shut up after that as Tim continued, but it never changed my mind  in thinking that threaded screw inserts for the coverplate holes are a great idea.

You're correct, of course, but not everyone has our nuanced touch. I've worked on too many with stripped holes that either need fixing, or, even worse, have been "fixed". On one memorable repair the guy had put a drop of epoxy in with the toothpick fillers. It did a great job of holding the coverplate. Getting it apart required some industrial-strength profanity to then discover the glued-in cone. Sucker didn't rattle, though.

Threaded inserts are a good thing for anything that will need to come apart during its lifespan.

Back to the OP - was 4-40 correct?

Here's a picture from an old Beard catalog. Looks like 4-40 to me. Maybe Paul would disclose where he gets the inserts.