Does glass around a bathtub or shower have to be tempered?

Yes — glazing in a tub or shower enclosure with its bottom edge less than 60 inches above the standing surface must be safety glazing (IRC R308.4.5).

Glazing in walls, enclosures, or fences that contain or face bathtubs, showers, hot tubs, spas, saunas, steam rooms, and pools is a hazardous location when the bottom exposed edge of the glass is less than 60 inches above any standing or walking surface (R308.4.5).

That captures most tub and shower doors and adjacent windows, which must be tempered or laminated safety glazing regardless of the pane size.

The 60-inch measurement is taken from the standing or walking surface, so a window set over a tub or tub deck is generally included.