Hey, Vanilla, how are you doing!
Yes, the only times before yesterday I'd been to Luss was by car, as you say a really busy fast road, never drove there myself, always got driven
The cycle path from Glasgow - it's all cycle path now , no need to go on the roads at all - is a piece of cake, until Dumbarton, when it becomes a bit rough, only if you have skinny tyres though
What I did is, from Bell's bridge, at SECC, follow the signposted route. Because I worked at Scotstoun Rugby stadium a couple of times (a turn off of the path) and knew the way, I went through the back of the SECC (where I work mostly) and stayed on the road until I joined the path at Scotstoun.
This only to avoid the pedestrians at the Crown Plaza, and the gravel stretch towards the new transport museum, but I could have avoided the road altogether.
From Scotstoun (lLoch Lomond is signed posted) you practically follow the signs all the way to Clydebank, you end up in the middle of the shopping centre, where you join the Forth and Clyde canal, really nice bit, up to Bowling Basin.
You need to cross roads a couple of times, but the signs are clear.
From Bowling you go up a wee hill, cross into a really nice path between trees all the way to Dumbarton, follows the railway.
There is even a little shop half way you can stop at.
From Dumbarton to Balloch it's a bit manure strewn at times (ha ha), still some beautiful scenery along the river Leven (if I remember correctly what my tourist guide said, the Leven is the fastest flowing river in Scotland, yes? )
From Balloch to Luss the path runs mostly along the busy road, with some detours along forest bits, all really nice to cycle through. A monster ascend when you come back from Luss, for a bit, not steep but never ending, puff puff!
Cycling folks living in the that area are really lucky: you can practically go along the paths from village to village, get off where you want, rejoin to go to the next Village/town.
Like a cycling ring road!