Of all places Wikipedia. So take it at face value.
Brief summary of the info indicates the .450 Bushmaster is a modified .45 Professional developed by LeMag Firearms. The parent cartridge is 1.77", where the .450 Bushmaster is 1.70" to handle the Hornady ballistic-tip bullet. Both are apparently based on the .284 case, with a rebated rim, presumably for use with the AR bolt.
A quick glance at the Handloader's Manual of Cartridge Conversions indicates the .284 Winchester measures 1.775" from the base up to the bottleneck. Therefore, it appears that the conversion is as simple as cutting the .284 at the bottleneck, and you have a .45 Professional round. Trim it to 1.70" and you have .450 Bushmaster brass. I don't know if neck reaming is necessary but it probably is.
The base of the .284 Winchseter is .473". Yes, that's the same as a .30-06/.308 family round. Therefore, one would expect that -06 brass couls be converted to .450 Bushmaster by "simply" cutting to 1.70".
Things that make you go HRM.
I can't find anything on the "45 Professional" parent cartridge no on the LeMAG company. Every search gets hits for "L E MAG" articles.
Here are the source quotes:
The .450 Bushmaster (parent cartridge is the 45 Professional) rifle/cartridge conversion, was developed by Tim LeGendre of LeMAG FIREARMS LLC., and licensed to Bushmaster Firearms International LLC., for production and distribution. LeGendre still retains ownership. The 450 Bushmaster is designed to be used in the standard M-16/AR-15 platform, using standard magazines.
Bushmaster asked Hornady to produce the 45 Professional ammunition for this project, Hornady agreed. Hornady wanted the 45 Professional shortened, to accommodate their Venerable 250gr., Pointed, SST bullet. Hornady asked Bushmaster for the change (1.771" to the now standard 1.700"), Bushmaster asked LeGendre to sign off on that change, and he did. Bushmaster eventually wanted a name change and LeGendre agreed, to what has now become the popular 450 BUSHMASTER.
Based on a concept by Col. Jeff Cooper (Thumper), the goal was to provide guaranteed one-shot kills on Big Game animals at 250 yards, with a large bore semi-auto (44 cal or larger). Col. Cooper upon being presented with the early 45 Professional stated??this is Thumper Senior?I can now own an AR-15?. A 45 Pro was indeed built for Col. Cooper, by LeMAG, pretty good considering his disdain for the AR-15 in 5.56 NATO. Hornady, with its extreme expertise, busted the Cooper 250yd limit. The result is the 450 BUSHMASTER, a semi-auto rifle/cartridge combination that absolutely provides more than enough stopping power to adequately kill all Big Game in North America.
I came across only one other reference on a blog page, again take it at face value:
It has been called to my attention that when I referred to the "45 Professional" cartridge dreamed up by Tim LeGendre, I should have said that it was based on the 284 case, rather than the 280 case. The 284, with its rebated rim, permits a slightly larger powder capacity than the 280.