Completed The Heist and the only vehicle I have (without going GTA) is Jackie's bike.
Handling is almost like Tron's light motorcycle game... as in the bike will only go in straight lines and is really hard to steer to follow the curve of the road.
We need look/steer with this.
Use 3rd-person view and use your mouse to control your camera position / angle. As for following the curve, don't go into a turn with way too excessive speed, then release throttle when entering the turn while holding A or D down. Once you see the bike doing suffuciently tight a turn - give it full throttle again.
You see, the bike is stable whenever you don't repeatedly tap A / D during a turn. Which is, in fact, indeed much how it is in real life - if you'd try any fancy twitchy moves of the front wheel while going any fast, IRL bike - it'll wobble and throw you out like a crazy bull. Unless you have lightning-fast reflexes of a moto-GP pilot and is lucky to "catch" the wobble before it gains too much amplitude. And you can see what i'm talking about - in the following video. Note how most of the time, problems begin exactly when pilots change how tight a turn the bike is about to do (i.e. starting or exiting a corner):