I was able to get the Bixby update after rebooting my watch. Press and hold bottom button for about 6-7 seconds (keep holding even when power off/touch sensitivity screen appears) until screen goes dark. Screen will come back on with 'rebooting' and will load as normal. This does not erase any settings or Samsung Pay data/cards already on the watch.
Rebooting and accepting the terms and the rest worked for me, too! So much better than resetting.
BTW, resetting it and restoring it isn't awful. At least it wasn't for me. I gave mine to my husband to try it for himself. When he bought one for himself, he gave it back to me and I restored from a backup.
Luckily, you may not need to do it for this situation but if it comes up again, it's not as bad as you fear.
Had the same issue - solved by rebooting watch as described above by userWoLTKoPz7D.
Here are the ugly details....
After the watch came back after reboot, hit Bixby on Wear app. The same Update Bixby message on watch. Hit update and got the Terms and Conditions change. Accepted the changes and finally success.