Organised beach bars and beach clubs in Montenegro generally have at least a basic toilet and a freshwater rinse shower — the more developed spots on busy beaches like Becici, Petrovac, or Budva's Slovenska Plaza usually include changing cabins and hot-water showers as well.
The picture is spottier at quieter or more remote beaches. Small coves on the Lustica peninsula (Zanjic, Mirista) or cliff-accessed spots may have only a portable toilet or none at all. Public beach zones — as opposed to a bar's private concession — sometimes have separate municipal facilities nearby, though quality varies.
A good rule of thumb: if a bar is renting out sunbeds and serving food, it almost certainly has a toilet. If you are uncertain, ask when you arrive or check the bar's Instagram before heading out — most established clubs post photos that make the setup clear.