My first thought is the bucket. Some of the plastic buckets out there are really toxic and the worms may be responding to that.
Of course there might always be those that run from their new environment. Ten isn't a horrible number. But if it gets worse, maybe just find a big cardboard box to put them in until their new house arrives.

Some quick related questions:

(1) When worms die from natural causes (age, disease, etc.), do they come up to the surface, or go to the very bottom?

(2) Do worm sometimes go to sleep and do not move at all?

(3) What's the indication of a dead worm? (color, shape)

Thanks.

I don''t have answers to any of your questions, unfortunately. The only dead worms I have ever seen are the dried up ones that have escaped and I have not found in time to put back in the bin.
I don't think though that they sleep.
If you really want to get their attention and give them a little boost until you can move them, put some watermelon or cantaloupe in there. Or even peaches. They love sweet fruit.

Thanks for the tip. Will the white portion of watermelon (less sweet) work? Our dog used to love them.
Indeed, this morning I found two dried worm bodies on the garage floor. One made 3 feet away from the bucket. Poor little worms' adventures.
There was also one worm lying on the surface, not moving for a good minute. However, once I gave it a little more sun light, it started wiggling down. Maybe some worms take night naps on the surface?