THIS GUIDE IS MORE AIMED TOWARDS THOSE HIT WITH THE BUG.
To get this achievement you will need to buy the Downtown Cab Co and then complete a private fare, which is not always the same fare IIRC. I would say that the best way to achieve this bug free would be buying the Cab Co ASAP, which should not long after completing some missions with Trevor and gaining back control of Michael & Franklin. You should receive what would be the 2nd call from Raul offering you the job, accept, quick save and complete.
Now of you've been hit with the bug and have tried everything else, this is what helped me.
Firstly, the only reasons I can see for the bug occurring for me was that I bought other properties first and then ignored the text to help out at "Pitchers" (property), after that I received no other calls across all characters. The other reason for the bug may have been a corrupted save location.
After this I decided to sleep and create a new save location, slept 5 more times and the made a booty call, as I was taking her back I got a call from the 1st place I bought - which I completed this time. I went and slept 6 times again after that and carried on with collectables, as I was approaching the Vinewood sign I got the call and then the achievement - The fare was to drive to the Vinewood sign, which might be telling so could be worth looking at spawn and finish locations for fares and then driving around the area.