No booking required as such, but still need to register and agreed to abide by a list of COVID-19 Safety Plan actions.
My understanding is that this currently applies to all NPWS and many other campsites, e.g. those on Crown Lands, including remote ones that don't charge fees.
https://www.nationalparks.nsw.gov.au/visit-a-park/parks/blue-mountains-national-park/local-alertsOther planned events: Six Foot Track - camping registration
If you're planning to stay at a campground managed by Crown Lands (e.g. on Six Foot Track) from 1 June 2020, you now need to fill out the Crown reserves camping registration form.
To register fill in the online form and submit.
This link can be emailed or sent by text message. The form can be submitted on a smartphone or computer.
This is required to comply with the Public Health Order and COVID-19 Safety Plans.
Here is the link to register for Six Foot Track campsites:
Crown reserves camping registration form