I would not use a bushing die for case forming. Get a full length sizing die.
On my 22BR, I went with the .243" neck chamber, mainly because I'm a masochist. The reduction in diameter is so great, I ended up turning it once as 6mm and then a finish turn as 22BR after first trimming a big chunk off the end to fit the 22BR chamber length. Some on this forum have gone with looser necks, some even no turn chambers. I believe some have even gone with no turn, no trim chambers and reported very good accuracy. There are so many flavors of 22BR out there, what you end up having to do will depend mainly on which chamber you have. However, form the cases with a regular 22BR FL sizing die.