I discovered tiny ball bearings in my hot tub. Where could they come from? The hot tub is working fine.

The ball bearings from your spa are from a roto head jet. Typically they are from one of the larger sized jets and they make the swivel action in the roto swirl jets function smoothly. You can determine which jet is coming apart by the loose function of the center nozzle. The jet can be removed and replaced to solve this problem. Most jets screw out but when they have deteriorated a lot, you may need plyers to take the jet out in pieces.

Whoa...
shotgun?
Lets hope it is the more common problem of deteriorating "Rotating" style of jets. They use ball bearings to assist the rapid spinning action when high speed jets are on.
Identify which jets are bad and replace.
Unfortunately, if one started to detiorate, then all of the rotating type of jets, will follow.

Check to see if those tiny ball bearings are lead. just rub them on paper. if so those would be shotgun pellets