Moving scores from one computer to another.

Just the same as you would take along any other file. Likely by copy and paste using removable media (like a USB stick) using your file explorer.

I see the following options:

• Copy the files to the respective other computer via USB drive before/after travelling.
• Never save your files to a computer's hard drive from MuseScore's Save dialog. Instead, always save your files to a dedicated USB drive directly that you can plug into one of your computers. This way, you won't have concurrent versions of the same file on different computers that need to be synced manually. This prevents "accidents" when you forget the manual syncing or if you forget that the latest version of a file is actually on the other computer and accidentally work with an outdated one.
• Use a platform like Dropbox that automatically syncs files for you.

You can upload in your musescore account, make the score private. Then use your other device and open it.
OR
Email
Or you can get a thumbdrive

FWIW, while you can certainly use flash drives for this, I would also consider using a cloud service like Dropbox or Google Drive that automatically syncs files on all your computers. Use Edit / Preferences to make that your default folder for scores.

This is only a viable option if you expect to always be online when you need to access the files, though. If your mobile service offers tethering, that's not necessarily an unreasonable assumption. Failing that, I'd go with the flash drive, but I'd still consider setting that as the default folder for scores. What you want to avoid is mistakes made due to copying files back and forth between hard drive and flash drive and forgetting which copy is more recent than which etc. It's most foolproof if you have only a single "logical" copy of the score. One actual physical copy on a flash drive is one way to do that, but thinking of the cloud service as the "master" copy and the copies on your computers as "shadows" of it that are automatically synced for you is really nice in that it doesn't require you to constantly swap out thst flash drive.