Hello,
Unfortunately the driver information is not stored anywhere within the DOS diagnostics. Even if this information were accessible, it would only show the generic drivers that are used within the DOS environment. These generic drivers wouldn't be useful in giving you any information on whether they are up to date or not.
As far as the Bootable goes, the information on the device drivers will be whichever ones Linux uses for the Bootable environment. Again, this may not be helpful in your scenario since the drivers used will typically be different than those used within the OS.
Please let me know if you have any further questions, I'd be happy to assist.
Thanks,
Channing