If you're heading west towards Chatswood and feel intimidated by the prospect of riding the bridge deck witht he traffic, you have an option, although it is slower and will test your climbing legs.
The footpath westbound on the *northern* (ie, your right hand going west) side of the road from Crown of The Hill Cellars, where the footbridge goes over Warringah Road at the top of the descent, is a Shared Use Path.
That will take you across the bridge and approximately halfway up the other side. You then do a U-turn, swing back down and around under the bridge and pop up on the other side, to continue climbing up to Babbage Road .
Just be aware that the climb back up from under the bridge to street level is a 40% pinch climb for about 50 metres, according to my Garmin. Good for seeing where your riding legs are at

The thought of having buses and tradies up my backside at 60+km/hr closing speeds tends to guarantee I take this route on weekday mornings.