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"(1) Explain how this happens when an experiment starts with a single bacterium..."

"(2) A single bacterium will either be immune to the antibiotic from the beginning or it will die. Duh!"

Either you are just joshing with him, or you really don't understand what is going on.

Experiments that start with a SINGLE BACTERIUM begin by growing a "culture", which is to say, zillions of the little critters, since they reproduce by fission.

If there were NO MUTATIONS as you suggest, at the end of growing the culture, you would have zillions of exact copies, and following that line to it's logical conclusion, they would either be immune to an anti-biotic under test, or they would all die.

SURPRISE! That is NOT what happens!. The copies are NOT all identical. There are errors in copying DNA strings. Most produce either no noticable effect, due to some interesting "error correction" in the sequencing for proteins. However, some produce beneficial changes, while others produce harmful ones.

What do we get? SOME bacteria are MORE RESISTANT to the anti-biotic under test, and live long enough to reproduce, thus transferring the beneficial trait on to the next generation.

It is TEXTBOOK evolution, in experimental form, repeatable as often as you care to.