To the best of my knowledge, Brownell's Screwdriver Bits are made by Apex. Apex makes the finest screwdriver bits I have ever used in my life; and that includes Snap-on! Apex still might sell direct if you buy a larger amounts (I used to, but no more), but for all practical purposes Brownells is the place for guys like us to get them from.
There are Wheeler, Grace, etc. that are OK, but the Brownell's (Apex) are simply the best IMHO. By the way, I have several sets of Brownell's Bits that I use for purposes other than on guns. Any time I care about not ruining a screw that is what I use. My Snap-on, Craftsman, Klien and Vaco screwdrivers are now pretty much decorating my tool box draws.
PS: I also have a complete set of Torx, Allen, Phillips (anti cam-out) square drive, etc. etc. from Apex as well. They are all many many years old and I have NEVER broken one. They are all in perfect condition and I DO use them almost every single day. Not only do I use them in Brownell's screwdriver handles, but I use them (with an Apex adaptor) with my 1/4" Ratchets - so they are NOT babied!
PS: I am a TOOL NUT and so there aren't too many brands out there (hand tools) that I haven't owned and/or tried. I'm sure there are some, but all the major brands and styles are either in my tool box or I've sold them. Not bragging, just being honest. I've spent way too much $$ on tools but at least now I feel I've got the best of the best.