My A2000 with Kickstart 3.1 rom and Workbench 3.9 works fine with it's Bridgeboard.
This is not helpfull.

You must have at least 68020 cpu. How have you setupped your bridgeboard software?
I have :
1. A2000 with 68030, ks 3.1 and Commodore 8088 bridgeboard (lattest bios)
Works, but time to time it just disappears. Couldn't setup up hard disk partition for it. File hard disk works just fine.
2. A500 with 68000, GVP Impact series II scsi with SCSI2SD, ks 3.1 and KCS Power PC board v2.
SetupHD program doesn't found any partitions, tried with 64mb, 512mb and 2gb sd cards.