You cant. The nature of bios updates these days are windows executables and when windows shuts down, there is no mechanism to input the bitlocker password without human intervention.
We're a Dell shop here and I push out bios updates all the time.
The main issue I see, is that BIOS update puts the PC into bitlocker recovery mode and the end user will need to input their recovery password.
Not an issue here since we only have a few bitlocker users and they keep their recovery passwords in print form and in their locked file cabinets.
Just spitballing here, but cant you use the Package Boot Helper in Patch Manger to run commands before and after the package installation?
Suspend Bitlocker (Win 8-10) - Suspend-BitLocker -MountPoint "C:" -RebootCount 5
Suspend Bitlocker (Win 7) - manage-bde -protectors -disable "C:"
Resume Bitlocker (Win 8-10) - Resume-BitLocker -MountPoint "C:"
Resume Bitlocker (Win 7) - manage-bde -protectors -enable "C:"
I never personally used these commands with Patch Manager, but I have with PDQ Deploy in conjunction with Office deployments.
I don't know if this info will help, but I hope it does.
Is the bios on all your PC's password protected? If so, how are you getting around the password to install the bios updates?