Lynne Neagle has expressed worries that young people will be prevented from having access to education and training.
MyTravelPass, which offered a third off bus travel, ended 18-months after it launched.
Labour Economy Secretary Ken Skates said he was hoping to launch a replacement for the pilot scheme.
Ms Neagle said it was encouraging that Mr Skates wanted a "legacy scheme" after Mytravelpass ends on 31 March.
Torfaen AM Ms Neagle told the Senedd earlier this week that she was "very disappointed that the Mytravelpass scheme was not going to be continued".
A reason given for ending the scheme was that young people were not using the pass to travel outside their immediate areas.
Ms Neagle told the chamber it was not "particularly surprising" that young people were using it to travel locally.
"My concern is that young people will be prevented from having access to education, training and youth services," she said.
Mr Skates responded: "The fact of the matter is that uptake was not as high as we would've wished, which is why I'm very keen for the successor programme to reach more young people across Wales."
He said he would want to see more than the 10,000 young people who used the pass to use the new scheme, which he promised to announce in coming weeks.
Ms Neagle told BBC Wales that she will seek assurances from the Welsh Government that any new scheme "is at least as good as the pilot scheme and that it is funded by Welsh Government and not by local authorities, who are already struggling because of UK government cuts".
Bus operators' body CPT Cymru have previously said the scheme was not well publicised and take-up had been low.
The Welsh Government has asked councils, bus operators and public transport information service Traveline Cymru to consider affordable ways of continuing to offer cheaper bus travel for young people.
The scrapping of a scheme to give 16-18 year olds discounted travel has prompted concerns from a Labour AM.