Are you sure that you are talking about a BIOS and not UEFI? Because if you are I need to start with a warning:
Upgrading the BIOS is somewhat risky. If the upgrade fails (e.g, due to a power failure mid re-flash) you end up with a bricked system. There are exceptions to this, e.g. expensive systems with two BIOS chips, or with a minimal backup BIOS which allows you to try to write the BIOS again, but those are not common.
Therefor the only regular reason to do do a BIOS upgrade usually is:
- The newer BIOS version has a new feature which you need.
- You want all systems to have the same BIOS version (which is not uncommon in large firms with hundred of identical systems, but which you will rarely encounter at home).
OK, having said that: Upgrading should be done with care. Risky stuff like IDE to SATA convertors should be avoided.
Which leaves you a few options:
- Do not upgrade the BIOS. Use the current one.
- Or get/borrow a SATA CD/DVDROM.
- Or risk it and hope that the adapter does things properly.
Personally I would use the already installed BIOS and just use it.