Transport is currently a bit more difficult than it has been in the past. The easiest option, if you have access to two cars, will be to organise a car shuttle with your walking buddies. In the app there are buttons to help find direct driving directions.

Katoomba Trackhead
Drive/ride: There is a car park at the trackhead. It is a sealed road to access, but the car park is dirt.
Train & Walk: It is a 2.6km (about 30min) walk from Katoomba Train Station to the Katoomba track head (near the Explorers Tree). The walk is mostly along footpaths and roads; there are some bush track options if you prefer.
Taxi and Uber: Uber prices will vary, it is about $10-15 from Katoomba Train Station to the Katoomba track head.

Megalong Valley Trackhead
No public Transport
Drive/ride: There is a car park at the trackhead on the side of the road. It is a sealed but windy road into Megalong Valley.
Taxi and Uber: Uber prices will vary greatly; it is about $60-90 from Katoomba and $40-60 from Blackheath. You may be able to book a ride from Megalong Valley out; just be aware of limited phone coverage (Telstra works) and have a back plan if the ride is cancelled.
There are no public transport options.

Coxs River Campsite
No public Transport
Limited 4WD access only: It is possible to drive a 4WD with high clearance to Coxs River Campsite; however, it is not recommended. The drive to Kiangatha Yards (halfway between Coxs River to Alum Creek) is a much better access point. Part of the road is dirt and has some ford crossings. It is a 55km, 1hr drive from Katoomba (Via LIttle Jartley, Coxs River Rd, Ganbenang Rd, Glen Chee Rd). (Warning: Some maps show an incorrect, dangerous and locked, direct access from Megalong Valley Rd, across Coxs River - You will need to drive via Little Hartley).

Black Range Campsite
No public Transport
Drive/ride: There is a car park beside the campsite. Most of the drive (62km, 1hr from Katoomba) is on sealed roads; the final 1.2km is along generally well-maintained dirt roads (slippery in the wet). The turn-off from Jenolan Caves Rd onto Black Range Trk (for the last 1.2km drive along dirt roads to the campsite) is not signposted.
There is no public transport and the uber app quotes $200 for the trip from Katoomba (if they will actually accept the ride).

Jenolan Caves
There’s no public transport to or from Jenolan Caves. If you plan to finish this walk at Jenolan, please arrange your own transport.
Drive/ride: Access to Jenolan is via Edith Road (2-Mile Road) only. This road is only suitable for vehicles smaller than a 12-seat minibus.

A minibus shuttle service can be arranged between Jenolan and the pick-up point for larger buses. The shuttle takes you to Kanangra Walls Road turnoff where you can meet your pre-arranged transport. Bookings can be made at Jenolan Caves House reception. Contact the Jenolan Caves office before you hike on 1300 76 33 11 to confirm cost and availability.

Driving access to Jenolan Cottages is unchanged.

Driving access to Jenolan Caves & Hotel (at the western end of the Six Foot Track) is currently by a signposted detour. The detours starts on Jenolan Caves Rd by turning right onto Duckmaloi Rd. After nearly 21 km, turn left onto Titania Rd, then after another 4.3 km, turn left onto Edith Rd. After another 18 km, you will come to a well-signposted stop gate, wait (for about 20 minutes) for the Transport NSW escort vehicle that you will then follow as you drive the final 3 km of narrow road to the Jenolan car parking area. From the car park, there is a 500m downhill walk to the caves and hotel.