Committee chairwoman Bethan Jenkins said it would "better reflect Welsh life" and AMs were pleased it was being considered by the corporation.
AMs also called for an extra Â£30m to be spent each year on BBC English-language drama and broadcasting about Wales.
The BBC said plans for more spending would be announced "in due course".
The broadcaster has previously conceded aspects of Welsh life had not been "sufficiently captured" by its TV services in Wales.
During its inquiry into the state of the broadcast media industry in Wales, BBC Director General Lord Hall told the Culture, Welsh Language and Communications Committee that putting Wales-based news bulletins on Radio 1 and 2 was being discussed as part of a review.
Ms Jenkins said her committee believed "flagship stations such as Radio 1 and Radio 2 should carry Wales-specific opt-outs for their news programmes to better reflect Welsh life".
AMs were "pleased to hear" this was being seriously considered, she added.
The committee's report said there should be no more funding cuts for S4C until an independent review of the channel had been completed.
It also called on ITV Wales to take a more proactive approach to getting its programmes broadcast across the ITV network.
A BBC spokeswoman said: "We've said that improving how we portray and represent the different nations of the UK - including Wales - on our UK-wide services is a priority for the new Charter period.
"As part of this we've committed to spending more on English-language television programming in Wales and will set out the proposals in due course."
Welsh listeners to BBC Radio 1 and 2 should hear news bulletins about Wales at certain times of the day, according to the assembly's culture committee.