One TD says a specific transport police unit should be set up within An Garda Síochána.
Fianna Fáil's justice spokesperson Jim O'Callaghan also believes authorities are not tough enough on anti-social behaviour.
The party has launched a consultation for people's views on the topic.
Deputy O'Callaghan told The Hard Shoulder this should have happened already.
"It is a big issue and I suppose it's something that we were aware of before the last election.
"In our manifesto we said that we wanted to introduce a specific public transport unit within An Garda Síochána to protect people using public transport."
He says there needs to be a consistent approach to this.
"One of the concerns people have is when they're using those forms of public transport, they don't believe there's any consistent or effective mechanism for security on them.
"Sometimes you might see security officers on a Luas, but in general it's a no-go area for the Gardaí when it comes to travelling on buses or on the DART or on the Luas."
He says currently, Gardaí might be stationed at transport stops - but not on the transport itself.
'People have to believe they're going to be protected'
The NBRU and Gardaí have been consulted on the issue.
Deputy O'Callaghan says the NBRU "would be very supportive of it", owing to threats to the safety of drivers and transport workers.
"We think that a specific public transport unit within An Garda Síochána should be established to protect public transport users.
"If there's legislation introduced or if a unit is established within the Gardaí, obviously then there would be a specific unit within the force directed towards transportation.
"They will do that if that occurs".
He adds: "When people use a form of public transport, they have to believe that they're going to be protected when they're using it.
"We see that in other cities where the public transport is very safe, because there's an awareness there if you get involved in anti-social behaviour... the authorities come down on you like a tonne of bricks.
"Unfortunately that doesn't appear to be the situation in Dublin, particularly, at present".
