A union representing NSW Transit bus drivers has raised the threat of industrial action unless its current wage claim is exempt from upcoming government legislation.

The Rail, Tram and Bus Union (RTBU) has seized on NSW government assurances that negotiations over police wages will be exempt from its planned industrial bill, which is being debated in the upper house.

After pressure from key crossbench MPs, the government has offered to exempt negotiations on the police award, which expires on June 30, from its public sector wage changes.

But with the award for State Transit Authority (STA) bus drivers expiring on June 11, the RTBU today met Transport Minister Gladys Berejiklian to demand it also be exempt.

RTBU division secretary Chris Preston said drivers' protests had so far been peaceful.