Hi nancycamb,
Welcome to Apple Support Communities! We'd love to help with installing Big Sur. Let's go over all options together.
As macOS Big Sur requires APFS, you'll want to format the external drive before attempting the install. The following guide has more information:
If you can’t install macOS on an external disk - Apple Support
We'd also like to share the following guide with further details:
File system formats available in Disk Utility on Mac - Apple Support
We're here for you if you've got any questions.
Have a great day!