Brisbane's Lord Mayor Graham Quirk said the Rail, Tram and Bus Union seemed intent on fighting the council's "fair" pay offers, and their planned industrial action would risk children's safety and inconvenience commuters.

At this stage, union-member bus drivers plan to go ahead with not taking fares on Thursday and walking off the job from 2pm and 6pm on Friday.

These bus service changes are part of the RTBU's ongoing strike action as they fight for safer buses, a wage increase and rostering changes.

Cr Quirk said the council paid bus drivers in accordance with the industry.

"I think we've got a fair offer on the table, most people in the community I think would see 2.5 per cent each year for three years plus a $400 sign on bonus to that increase pretty reasonable." he said.

"I believe that it's a reasonable offer, a good offer and I don't believe what we're seeing with industrial action is a good thing for our city...but I also don't think it's reasonable action in light of the offer."

RTBU secretary Tom Brown said the union met with the council on Tuesday, but the meeting was unfruitful.

The RTBU had previously knocked back the council's offer of a 2.5 per cent pay increase and $400 signing bonus, but had not made a counter-offer.

At the meeting on Tuesday the union said they wanted a basic pay percentage increase of 3.5 per cent - about $1 an hour - on top of a reshuffled wage progression.

"Bus drivers are very poorly paid,"Mr Brown said.

"It takes nine years for a bus driver to work through the wage levels from a low $22.90 up to the high point of $27."

Cr Quirk said the council would not budge on their offer.

RTBU secretary Tom Brown said bus drivers were left with no choice but to escalate their strike action and alleged the Brisbane City Council refused to negotiate with bus drivers over their concerns.

"I am calling on BCC to get back to the table, the time for hiding is over, it's time to negotiate the end of this dispute," Mr Brown said.

The council's public transport boss Adrian Schrinner said the union's strike action would risk the safety of up to 23,000 school children and inconvenience a further 115,000 passengers.

Mr Schrinner asked union bus drivers to put the safety of children first.

"While the school run services will be our operational priority, most school children catch normal bus services," he said.

"We remain hopeful that most drivers will perform normal services as the majority bravely did during last week's industrial action."

Mr Brown said he didn't expect the impacts of the strike to be as bad as the council had speculated.

"I'm quite sure that council has contingency plans in place and I am quite sure that drivers will be made available to prioritise school children during those hours," he said.

Mr Brown said if the council brought a fair offer to the table, strike action could be avoided.

"We're hoping for the best, but preparing for the worst," he said.

Mr Brown did not rule out strike action further escalating to services leaving the road for entire days.

"We will take each step as it comes, but our next steps will be entirely based on council's reaction," he said.

The RTBU will meet with the council on August 1 to discuss bus driver safety.

Commuters were encouraged to plan ahead, by checking the TransLink app, website or contacting 13 12 30 for up-to-date information and make alternative arrangements if necessary.